Optimization

Topics are

• Convex Analysis
• Invexity
• Differentiability and Subdifferentiability
• Karush-Kuhn-Tucker Conditions
• Optimality Conditions
• Nonsmooth Optimization Problems
• Numerical Methods for Optimization Problems
• Duality Theory
• Parametric Programming
• Large-Scale Optimization
• Fractional Programming
• Goal Programming
• Continuous-Time Programming Problems
• Inverse Optimization
• Dynamic Programming
• Minmax Regret Optimization
• Multi-level Optimization
• Second-Order Cone Programming
• Semi-Infinite Programming
• Set Optimization
• Stochastic Optimization
• Robust Optimization
• Neural Network for Optimization
• Vector Optimization
• Optimization for Interval-Valued Functions
• Optimization for Set-Valued Functions
• Uncategorized

\begin{equation}{\label{a}}\tag{A}\mbox{}\end{equation}

Convex Analysis.

\item Asplund, E. \& Rockafellar, R.T. :
Gradients of Convex Functions,
{\em Trans. Amer. Math.} 139 (1969) 443-467.

\item Avriel, M.:
$r$-Convex Functions,
{\em Mathematical Programming} 2 (1972) 309-323.

\item Bianchi, M., Hadjisavva, N. \& Schaible, S. :
Vector Equilibrium Problems with Generalized Monotone Bifunctions,
{\em J. Optimization Theory and Applications} 92 (1997) 527-542.

\item Bianchi, M. \& Schaible, S. :
Generalized Monotone Bifunctions and Equilibrium Problems,
{\em J. Optimization Theory and Application} 90 (1996) 31-43.

\item Bitran, G.R. \& Magnanti, T.L. :
The Structure of Admissible Points with Respect to Cone Dominance,
{\em J. Optimization Theory and Applications} 29 (1979) 573-614.

\item Borwein, J.M. :
A Lagrange Multiplier Theorem and a Sandwich Theorem for Convex Relations,
{\em Math. Scand.} 48 (1981) 189-204.

\item Borwein, J.M. :
Continuity and Differentiability Properties of Convex Operators,
{\em Proc. London Math. Soc.} (3) 44 (1982) 420-444.

\item Br$\not o$ndsted, A. :
Conjugate Convex Functions in Topological Vector Spaces,
{\em Mat.-fys. Medd. Dansk. Vid. Selsk.} 34 (1964).

\item Br$\not o$ndsted, A. \& Rockafellar, R.T. :
On the Subdifferentiability of Convex Functions,
{\em Proc. Amer. Math. Soc.} 16 (1965) 605-611.

\item Browder, F.E. :
Nonlinear Monotone Operators and Convex Sets in Banach Spaces,
{\em Bull. Amer. Math. Soc.} 17 (1965) 780-785.

\item Browder, F.E. \& Hess, P. :
Nonlinear Mappings of Monotone Type in Banach Spaces,
{\em J. Functional Analysis} 11 (1972) 251-294.

\item Clarke, B.R. :
Nonsmooth Analysis and Fr\'{e}chet Differentiability of M-Functionals,
{\em Probability Theory and Related Fields} 73 (1986) 197-209.

\item Correa, R., Jofr\'{e}, A. \& Thibault, L. :
Characterization of Lower Semicontinuous Convex Functions,
{\em Proc. Amer. Math. Soc.} 116 (1992) 67-72.

\item Craven, B.D. \& Mond, B. :
Transpositin Theorems for Cone-Convex Functions,
{\em SIAM J. Appl. Math.} 24 (1973) 603-612.

\item Elluia, R. \& Hassouni, A. :
Characterization of Nonsmooth Functions through Their Generalized Gradients,
{\em Optimization} 22 (1991) 401-416.

\item Fan, K. :
A Minimax Inequality and Applications, In {\em Inequalities III}
(edited by Shisha, O.L.), pp.103-113, Academic Press, NY, 1972.

\item Fenchel, W. :
On Conjugate Convex Function,
{\em Canadian J. Math.} 1 (1949) 73-77.

\item Gallego, G. and Sethi, S.P.:
${\cal K}$-Convexity in $I\!\! R^{n}$,
{\em Journal of Optimization Theory and Applications} 127 (2005) 71-88.

\item Gwinner, J. :
Results of Farkas Type,
{\em Numer. Funct. Anal. and Optimz.} 9 (1987) 471-520.

\item Ha, C.-W. :
On Systems of Convex Inequalities
{\em J. Math. Anal. Appl.} 68 (1979) 25-34.

\item Hadjisavas, N. \& Schaible, S. :
On Strong Pseudomonotonicity and (Semi)stricy Quasimonotonicity,
{\em J. Optimization Theory and Applications} 79 (1993) 139-155.

\item Hartley, R. :
On Cone-Efficiency, Cone-Convexity and Cone-Compactness,
{\em SIAM J. Appl. Math.} 34 (1978) 211-222.

\item Holtzman, J.M. \& Halkin, H. :
Directional Convexity and the Maximum Principle for Discrete Systems,
{\em SIAM J. Control} 4 (1966) 263-275.

\item Jeyakumar, V. :
A Generalization of a Minimax Theorem of Fan via a Theorem of the Alternative,
{\em J. Optimization Theory and Applications} 48 (1986) 525-533.

\item Karamardian, S. \& Schaible, S. :
Seven Kinds of Monotone Maps,
{\em J. Optimization Theory and Applications} 66 (1990) 37-46.

\item Karamardian, S., Schaible, S. \& Crouzeix, J.P. :
Characterizations of Generalized Monotone Maps,
{\em J. Optimization Theory and Applications} 76 (1993) 399-413.

\item Hartwig, H. :
Generalized Convexities of Lower Semicontinuous Functions,
{\em Optimization} 16 (1985) 663-668.

\item Jameson, G.J.O. :
Convex Series,
{\em Proc. Camb. Phil. Soc.} 72 (1972) 37-47.

\item Kato, T. :
Demicontinuity, Hemicontinuity and Monotonicity,
{\em Bull. Amer. Math. Soc.} 70 (1964) 548-550; 73 (1967) 886-889.

\item Kien, B.T., Liou, Y.C., Wong, N.-C and Yao, J.-C.:
Subgradients of Value Functions in Parametric Dynamic Programming,
{\em European Journal of Operational Research} 193 (2009) 12-22.

\item Klee, V.L. :
Separation Properties of Convex Cones,
{\em Proc. Amer. Math. Soc.} 6 (1955) 313-318.

\item Klee, V.L. :
The Critical Set of a Convex Body,
{\em American J. Math.} 16 (1968) 178-188.

\item Lasserre, J.B. :
A Farkas Lemma without a Standard Closure Condition,
{\em SAIM J. Control Optim} 35 91997) 265-272.

\item Luc, D.T. :
Characterizations of Quasiconvex Functions,
{\em Bull. Austral, Math. Soc.} 48 (1993) 393-406.

\item Luc, D.T. :
On Generalized Convex Nonsmooth Functions,
{\em Bull. Austral, Math. Soc.} 49 (1994) 139-149.

\item McLinden, L. :
Affine Minorants Minimization the Sum of Convex Functions,
{\em J. Optimization Theory and Applications} 24 (1978) 569-583.

\item Minty, G.J. :
On the Monotonicity of the Gradient of a Convex Function,
{\em Pacific J. Math.} 14 (1964) 243-247.

\item Pang, J.-S. \& Yao, J.-C. :
On a Generalization of a Normal Map and Equation,
{\em SIAM J. Control Optimization} 33 (1995) 168-184.

\item Penot, J.P. :
Mean-Value Theorem with Small Subdifferentials,
{\em J. Optimization Theory and Applications} 94 (1997) 209-221.

\item Penot, J.P. \& Sach, P.H. :
Generalized Monotonicity of Subdifferentials and Generalized Convexity,
{\em J. Optimization Theory and Applications} 94 (1997) 251-262.

\item Poliquin, R.A. :
Subgradient Monotonicity and Convex Functions,
{\em Nonlinear Analysis} 14 (1990) 305-317.

\item Ponstein, J. :
Seven Kinds of Convexity,
{\em SIAM Review} 9 (1967) 115-119.

\item R\.{a}dstr\”{o}m, H. :
An Embedding Theorem for Spaces of Convex Sets,
{\em Proc. Amer. Math. Soc.} 3 (1952) 165-169.

\item Reiland, T.W. :
Nonsmooth Invexity,
{\em Bull. Austral. Math. Soc.} 42 (1990) 437-446.

\item Reinoza, A. :
The Strong Positivity Conditions,
{\em Mathematics of Operations Research} 10 (1985) 54-62.

\item Resentnjak, Ju. G.:
Generalized Derivatives and Differentiability Almost Everywhere,
{\em Math. USSR-Sbornik} 4 (1968) 293-302.

\item Robinson, S.M. :
Normed Convex Processes,
{\em Trans. Amer. Math. Soc.} 174 (1972) 127-140.

\item Robinson, S.M. :
Stability Theory for Systems of Inequalities, Part II : Differentiable
Nonlinear Systems,
{\em SIAM J. Numer. Anal.} 13 (1976) 497-513.

\item Robinson, S.M. :
Strong Regular Generalized Equations,
{\em Mathematics of Operations Research} 5 (1980) 43-62.

\item Robinson, S.M. :
Strong Regular Generalized Equations,
{\em Mathematics of Operations Research} 5 (1980) 43-62.

\item Rockafellar, R.T. :
Minimax Theorems and Conjugate Saddle-Functions,
{\em Math. Scand.} 14 (1964) 151-173.

\item Rockafellar, R.T. :
Helley’s Theorem and Minima of Convex Functions,
{\em Duke Math. J.} 32 (1965) 381-398.

\item Rockafellar, R.T. :
Level Sets and Continuity fo Conjugate Convex Functions,
{\em Trans. Amer. Math. Soc.} 123 (1966) 46-63.

\item Rockafellar, R.T. :
Local Boundedness of Nonlinear Monotone Operators,
{\em Michigan Math. J.} 33 (1966) 81-89.

\item Rockafellar, R.T. :
Characterization of the Subdifferentials of Convex Functions,
{\em Pacific J. Math} 17 (1966) 497-510.

\item Rockafellar, R.T. :
Conjugates and Legendre Transforms of Convex Functions,
{\em Canadian J. Math.} (1967) 200-205.

\item Rockafellar, R.T. :
Integrals which are Convex Funtionals,
{\em Pacific J. Math} 24 (1968) 525-539.

\item Rockafellar, R.T. :
Measurable Dependence of Convex Sets and Functions on Parameters,
{\em J. Math. Anal. Appl.} 28 (1969) 4-25.

\item Rockafellar, R.T.
Monotone Operators Associated with Saddle-Functions and Minimax Problems,
{\em Nonlinear Functional Analysis}, Part 1, Browder, F.E., (ed.) Symposia
in Pure Math. Vol. 18, Amer. Math. Soc., Providence, RI, 1970, pp.241-250.

\item Rockafellar, R.T. :
On the Maximal Monotonicity of Subdifferential Mappings,
{\em Pacific J. Math} 33 (1970) 209-216.

\item Rockafellar, R.T. :
Generalized Hamiltonian Equations for Convex Problem of Lagrange,
{\em Pacific J. Math} 33 (1970) 411-427.

\item Rockafellar, R.T. :
On the Maximality of Sums of Nonlinear Monotone Operators,
{\em Trans. Amer. Math. Soc.} 149 (1970) 75-88.

\item Rockafellar, R.T. :
Conjugate Convex Functions in Optimal Control and the Calculus of Variations,
{\em J. Math. Anal. Appl.} 32 (1970) 174-222.

\item Rockafellar, R.T. :
Integrals which are Convex Funtionals II,
{\em Pacific J. Math} 39 (1971) 439-469.

\item Rockafellar, R.T. :
State Constraints in Convex Control Problems of Bolza,
{\em SIAM J. Control} 10 (1972) 691-715.

\item Rockafellar, R.T. :
Monotone Operators and the Proximal Point Algorithm,
{\em SIAM J. Control and Optimization} 14 (1976) 877-898.

\item Rockafellar, R.T. :
Directionally Lipschitzian Functions and Subdifferential Calculus,
{\em Proc. London Math. Soc.} (3) 39 (1979) 331-355.

\item Rockafellar, R.T. :
Generalized Directional Derivatives and Subgradients of Nonconvex Functions,
{\em Canadian J. Math.} 32 (1980) 257-280.

\item Rockafellar, R.T. :
Generalized Seconf Derivatives of Convex Functions and Saddle Functions,
{\em Trans. Amer. Math. Soc.} 322 (1990) 51-77.

\item R\”{o}dder, W. :
A Generalized Saddlepoint Theory,
{\em European J. Operational Research} 1 (1977) 55-59.

\item Telgen, J. :
Minimal Represntation of Convex Polyhedral Sets,
{\em J. Optimization Theory and Applications} 38 (1982) 1-24.

\item Wagner, D.H. :
Semi-Compactness with Respect to a Euclidean Cone,
{\em Canadian J. Math.} 29 (1977) 29-36.

\item Wijsman, R.A. :
Convergence of Sequences of Convex Sets, Cones and Functions,
{\em Bull. Amer. Math. Soc.} 70 (1964) 186-188.

\item Wijsman, R.A. :
Convergence of Sequences of Convex Sets, Cones and Functions, II,
{\em Trans. Amer. Math. Soc.} 123 (1966) 32-45.

\item Zhang, X. :
Some Intersection Theorems and Minimax Inequalities,
{\em J. Optimization Theory and Applications} 94 (1997) 195-207.

\item Zowe, J. :
Subdifferentiability of Convex Functions with Values in an Ordered Vector
Space,
{\em Math. Scand.} 34 (1974) 69-83.

\begin{equation}{\label{b}}\tag{B}\mbox{}\end{equation}

Invexity.

\begin{enumerate}

\item Aghezzaf, B. and Hachimi, M.:
Generalized Invexity and Duality in Multiobjective Programming Problems,
{\em Journal of Global Optimization} 18 (2000) 91-101.

\item Antczak, T.:
$(p,r)$-Invex Sets and Functions,
{\em Journal of Mathematical Analysis and Applications} 263 (2001) 355-379.

\item Antczak, T.:
On $(p,r)$-Invexity-Type Nonlinear Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 264 (2001) 382-397.

\item Antczak, T.:
Multiobjective Programming under $d$-Invexity,
{\em European Journal of Operational Research} 137 (2002) 28-36.

\item Antczak, T.:
$(p,r)$-Invexity in Multiobjective Programming,
{\em European Journal of Operational Research} 152 (2004) 72-87.

\item Bector, C.R. :
Wolfe-Type Duality Invloving $(B,\eta )$-Invex Functions for a Minimax
Programming Problem,
{\em J. Math. Anal. Appl.} 201 (1996) 114-127.

\item Ben-Israel, A. and Mond, B.:
What is Invexity?
{\em Journal of Australian Math. Soc.} Ser. B, 28 (1986) 1-9.

\item Bhatia, D. and Garg, P.K.:
$(V,\rho )$ Invexity and Non-Smooth Multiobjective Programming,
{\em Recherche Op\'{e}eationnelle/Operations Research} 32 (1998) 399-414.

\item Bhatia, D. and Sharma, A.:
New-Invexity Type COnditions with Applications to Constrained Dynamic Games,
{\em European Journal of Operational Research} 148 (2003) 48-55.

\item Chandra, S.:
A Note on Pseudo-Invexity and Duality in Nonlinear Programming,
{\em European Journal of Operational Research} 122 (2000) 161-165.

\item Craven, B,D,:
Invex Functions and Constrained Local Minima,
{\em Bull. Austral. Math. Soc.} 24 (1981) 357-366.

\item Craven, B.D. and Glover, B.M.:
Invex Functions and Duality,
{\em Journal of Australian Math. Soc.} Ser. A, 39 (1985) 1-20.

\item Das, L.N. and Nanda, S.:
Proper Efficiency Conditions and Duality for Multiobjective Programming
Problems Involving Semilocally Invex Functions,
{\em Optimization} 34 (1995) 43-51.

\item Egudo, R.R. and Hanson. M.A.:
Multiobjective Duality with Invexity,
{\em Journal of Mathematical Analysis and Applications} 126 (1987) 469-477.

\item Fulga, C. and Preda, V.:
Nonlinear Programming with E-Preinvex and Local E-Preinvex Functions,
{\em European Journal of Operational Research} 192 (2009) 737-743.

\item Kaul, R.N., Suneja, S.K. and Srivastava, M.K. :
Optimality Criteria and Duality in Multiple-Objective Optimization Involving
Generalized Invexity,
{\em J. Optimization Theory and Applications} 80 (1994) 465-482.

\item Liu, J.C. :
Optimality and Duality for Generalized Fractional Programming Involving
Nonsmooth Pseudoinvex Functions,
{\em J. Math. Anal. Appl.} 202 (1996) 667-685.

\item Martin, D.H.: (E-Articles)(Print)
The Essence of Invexity,
{\em Journal of Optimization Theory and Applications} 47 (1985) 65-76.

\item Mishra, S.K.:
Non-Differentiable Higher-Order Symmetric Duality in Methematical Programming with Generalized Invexity,
{\em European Journal of Operational Research} 167 (2005) 28-34.

\item Nahak, C. and Nanda, S.:
Symmetric Duality with Pseudo-Invexity in Variational Problems,
{\em European Journal of Operational Research} 122 (2000) 145-150.

\item Nanda, S. and Das, L.N.:
Pseudo-Invexity and Duality in Nonlinear Programming,
{\em European Journal of Operational Research} 88 (1996) 572-577.

\item Noor, M.A.:
Invex Equilibrium Problems,
{\em Journal of Mathematical Analysis and Applications} 302 (2005) 463-475.

\item Peng, J.-W.:
Criteria for Generalized Invex Monotonicities without Condition C,
{\em European Journal of Operational Research} 170 (2006) 667-671.

\item Reiland, T.W. :
Nonsmooth Invexity,
{\em Bull. Austral. Math. Soc.} 42 (1990) 437-446.

\item Sach, P.H. and Craven, B.D. :
Invex Multifunctions and Duality,
{\em Numer. Funct. Anal. and Optim.} 12 (1991) 575-591.

\item Stancu-Minasian, I.M.:
Optimality and Duality in Nonlinear Programming Involving Semilocally B-Preinvex and Related Functions,
{\em European Journal of Operational Research} 173 (2006) 47-58.

\item Suneja, S.K., Khurana, S. and Vani,
Generalized Nonsmooth Invexity over Cone in Vector Optimization,
{\em European Journal of Operational Research} 186 (2008) 28-40.

\item Syau, Y.-R.:
Preinvex Fuzzy Mapping,
{\em Computesr and Mathematics with Applications} 37 (1999) 31-39.

\item Syau, Y.-R.:
Invex and Generalized Convex Fuzzy Mappings,
{\em Fuzzy Sets and Systems} 115 (2000) 455-461.

\item Syau, Y.-R.:
Generalization of Preinvex and B-invex Fuzzy Mappings,
{\em Fuzzy Sets and Systems} 120 (2001) 533-542.

\begin{equation}{\label{c}}\tag{C}\mbox{}\end{equation}

Differentiability and Subdifferentiability.

\item Amahroq, T., Penot, J.-P. and Syan, A.:
On the Subdifferentiability of the Difference of Two Functions and Local Minimization,
{\em Set-Valued Analysis} 16 (2008) 413-427.

\item An, P.T.:
Nonemptiness of Approximate Subdifferentials of Midpoint $\delta$-Convex Functions,
{\em Numerical Functional Analysis and Optimization} 26 (2005) 735-738.

\item Aussel, D.:
Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach,
{\em Journal of Optimization Theory and Applications} 97 (1998) 29-45.

\item Aussel, D., Corvellec, J.-N. and Lassonde, M.:
Subdifferential Characterization of Quasiconvexity and Convexity,
{\em Journal of Convex Analysis} 1 (1994) 195-201.

\item Azagra, D., Ferrera, J. and Sanz, B.:
Fixed Points and Zeros for Set-Valued Mappings on Riemannian Manifolds: A Subdifferential Approach,
{\em Set-Valued Analysis} 16 (2008) 581-596.

\item Bector, C.R., Chandra, S. and Husain, I. :
Optimality Conditions and Duality in Subdifferentiable Multiobjective Frational Programming,
{\em J. Optimization Theory and Applications} 79 (1993) 105-125.

\item Benoist, J. and Hiriart-Urruty, J.-B.:
What is the Subdifferential of the Closed Convex Hull of a Function,
{\em SIAM Journal of Mathematical Analysis} 27 (1996) 1661-1679.

\item Bigi, G. and Castellani, M.:
K-Epiderivatives for Set-Valued Functions and Optimization,
{\em Mathematical Methods of Operations Research} 55 (2002) 401-412.

\item Birge, J.R. and Qi, L. :
Subdifferential Convergence in Stochastic Programs,
{\em SIAM J. Optimization} 5 (1995) 436-453.

\item Bonnisseau, J.-M. and Van, C.L.:
On the Subdifferentiable of the Value Function in Economic Optimization Problems,
{\em Journal of Mathematical Economics} 25 (1996) 55-73.

\item Borwein, D., Borwein, J.M. and Wang, X.:
Approximate Subgradients and Coderivatives in $\mathbb{R}^{n}$,
{\em Set-Valued Analysis} 4 (1996) 375-398.

\item Borwein, J.M. and Fitzpatrik, S.:
Weak* Sequential Compactness and Bornological Limit Derivatives,
{\em Journal of Convex Analysis} 2 (1995) 59-67.

\item Borwein, J.M. and Zhu, Q.J.:
Limiting Convex Examples for Nonconvex Subdifferential Calculus,
{\em Journal of Convex Analysis} 5 (1998) 221-235.

\item Br$\not o$ndsted, A. and Rockafellar, R.T. :
On the Subdifferentiability of Convex Functions,
{\em Proc. Amer. Math. Soc.} 16 (1965) 605-611.

\item Campa, I. and Degiovanni, M.:
Subdifferential Calculus and Nonsmooth Critical Point Theory,
{\em SIAM Journal on Optimization} 10 (2000) 1020-1048.

\item Cornejo, O., Jourani, A. and Z\v{a}linescu, C.:
Conditioning and Upper-Lipshcitz Inverse Subdifferentials in Nonsmooth Optimization Problems,
{\em Journal of Optimization Theory and Applications} 95 (1997) 127-148.

\item Daniilidis, A. and Hadjisavvas, N. and Mart\'{i}nez-Legaz, J.-E.:
An Appropriate Subdifferential for Quasiconvex Functions,
{\em SIAM Journal on Optimization} 12 (2001) 407-420.

\item Daniilidis, A. and Jules, E. and Lassonde, M.:
Subdifferential Characterization of Approximate Convexity: The Lower Semicontinuous Case,
{\em Mathematical Programming} Ser. B 116 (2009) 115-127.

\item Dempe, S.:
Directional Differentiability of Optimal Solutions under Slater’s Condition,
{\em Mathematical Programming} 59 (1993) 49-69.

\item Demyanov, V.F. and Roshchina, V.A.:
Optimality Conditions in Terms of Upper and Lower Exhausters,
{\em Optimization} 55 (2006) 525-540.

\item Demyanov, V.F. and Roshchina, V.A.:
Exhausters and Subdifferentials in Non-smooth Analysis,
{\em Optimization} 57 (2008) 41-56.

\item Demyanov, V.F. and Roshchina, V.A.:
Exhausters, Optimality Conditions and Related Problems,
{\em Journal of Global Optimization} 40 (2008) 71-85.

\item El Haddad, E. and Deville, R.:
The Viscosity Subdifferential of the Sum of Two Functions in Banach Spaces I: First Order Case,
{\em Journal of Convex Analysis} 3 (1996) 295-308.

\item El Maghri, M. and Laghdir, M.:
Pareto Subdifferential Calculus for Convex Vector Mappings and Applications to Vector Optimization,
{\em SIAM Journal on Optimization} 19 (2009) 1970-1994.

\item Gao, Y.:
Newton Methods for Quasidifferentiable Equations and Their Convergence,
{\em Journal of Optimization Theory and Applications} 131 (2006) 417-428.

\item Glover, B.M. and Craven, B.D.:
A Fritz John Optimality Condition Using the Approximate Subdifferential,
{\em Journal of Optimization Theory and Applications} 82 (1994) 253-265.

\item Gretsky, N.E., Ostroy, J.M. and Zame, W.R.:
Subdifferentiability and the Duality Gap,
{\em Positivity} 6 (2002) 261-274.

\item Hantoute, A., L\'{o}pez, M.A. and Z\v{a}linescu, C.:
Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach via Pointwise Supremum Functions,
{\em SIAM Journal on Optimization} 19 (2008) 863-882.

\item Ivanov, M. and Zlateva, N.:
A New Proof of the Integrability of a Convex Function on a Banach Space,
{\em Proceedings of the American Mathematical Society} 136 (2008) 1787-1793.

\item Jahn, J. and Khan, A.A.:
Generalized Contingent Epiderivatives in Set-Valued Optimization: Optimality Conditions,
{\em Numerical Functional Analysis and Optimization} 23 (2002) 907-831.

\item Jahn, J. and Khan, A.A.:
Some Calculus Rules for Contingent Epiderivatives,
{\em Optimization} 52 (2003) 113-125.

\item Jahn, J. and Rauh, R.:
Contingent Epiderivatives and Set-Valued Optimization,
{\em Mathematical Methods of Operations Research} 46 (1997) 193-211.

\item Jourani, A. and Thibault, L.:
Metric Regularity and Subdifferential Calculus in Banach Spaces,
{\em Set-Valued Analysis} 3 (1995) 87-100.

\item Mart\'{i}nez-Legaz, J.-E. and Sach, P.H.:
A New Subdifferential in Quasiconvex Analysis,
{\em Journal of Convex Analysis} 6 (1996) 1-11.

\item Moors, W.B.:
A Characterization of Minimal Subdifferential Mappings of Locally Lipschitz Functions,
{\em Set-Valued Analysis} 3 (1995) 129-141.

\item Mordukhovich, B.S:
Generalized Differential Calculus for Nonsmooth and Set-Valued Mappings,
{\em Journal of Mathematical Analysis and Applications} 183 (1994) 250-288.

\item Mordukhovich, B.S:
Coderivatives of Set-Valued Mappings: Calculus and Applications
{\em Nonlinear Analysis, Theory, Methods and Applications} 30 (1997) 3059-3070.

\item Mordukhovich, B.S., Nam, N.M. and Yen, N.D.:
Fr\'{e}chet Subdifferential Calculus and Optimality Conditions in Nondifferentiable Programming,
{\em Optimization} 55 (2006) 685-708.

\item Mordukhovich, B.S. and Shao, Y.:
On Nonconvex Subdifferential Calculus in Banach Spaces,
{\em Journal of Convex Analysis} 2 (1995) 211-227.

\item Mordukhovich, B.S. and Shao, Y.:
Fuzzy Calculus for Coderivatives of Multigunctions,
{\em Nonlinear Analysis, Theory, Methods and Applications} 29 (1997) 605-626.

\item Ngai, H.V. and Th\'{e}ra, M.:
A Fuzzy Necessary Optimality Condition for Non-Lipschitz Optimization in Asplund Spaces,
{\em SIAM Journal on Optimization} 12 (2002) 656-668.

\item Outrata, J.V. and Sun, D.:
On the Coderivative of the Projection Operator onto the Second-Order Cone,
{\em Set-Valued Analysis} 16 (2008) 999-1014.

\item Penot, J.-P.:
Subdifferential Calculus Without Qualification Assumptions,
{\em Journal of Convex Analysis} 3 (1996) 207-219.

\item Penot, J.-P. :
Mean-Value Theorem with Small Subdifferentials,
{\em J. Optimization Theory and Applications} 94 (1997) 209-221.

\item Penot, J.-P. and Sach, P.H. :
Generalized Monotonicity of Subdifferentials and Generalized Convexity,
{\em J. Optimization Theory and Applications} 94 (1997) 251-262.

\item Penot, J.-P. and Z\v{a}linescu, C.:
Elements of Quasiconvex Subdifferential Calculus,
{\em Journal of Convex Analysis} 7 (2000) 243-269.

\item Plastria, F. :
Lower Subdifferentiable Functions and Their Minimization by Cutting Planes,
{\em Journal of Optimization Theory and Applications} 46 (1985) 37-53.

\item Pokorn\'{y}, D.:
The Approximate and the Clarke Subdifferentials Can be Different Everywhere,
{\em Journal of Mathematical Analysis and Applications} 347 (2008) 652-658.

\item Poliquin, R.A. :
Subgradient Monotonicity and Convex Functions,
{\em Nonlinear Analysis} 14 (1990) 305-317.

\item Poliquin, R.A. and Rockafellar, R.T.:
Proto-Derivatives of Partial Subgradient Mappings,
{\em Journal of Convex Analysis} 4 (1997) 221-234.

\item Precupanu, T. and Stamate, C.:
Approximate Quasi-Subdifferentials,
{\em Optimization} 56 (2007) 339-354.

\item Rockafellar, R.T. : (E-Articles and Prints)
Characterization of the Subdifferentials of Convex Functions,
{\em Pacific J. Math} 17 (1966) 497-510.

\item Rockafellar, R.T. : (E-Articles and Prints)
On the Maximal Monotonicity of Subdifferential Mappings,
{\em Pacific J. Math} 33 (1970) 209-216.

\item Rockafellar, R.T. :
Directionally Lipschitzian Functions and Subdifferential Calculus,
{\em Proc. London Math. Soc.} (3) 39 (1979) 331-355.

\item Rockafellar, R.T. :
Generalized Directional Derivatives and Subgradients of Nonconvex Functions,
{\em Canadian J. Math.} 32 (1980) 257-280.

\item Rockafellar, R.T. :
Generalized Second Derivatives of Convex Functions and Saddle Functions,
{\em Trans. Amer. Math. Soc.} 322 (1990) 51-77.

\item Romano, M.:
New Results in Subdifferential Calculus with Applications to Convex Optimization,
{\em Applied Mathematics and Optimization} 32 (1995) 213-234.

\item Roshchina, V.:
Relations between Upper Exhausters and the Basic Subdifferential in Variational Analysis,
{\em Journal of Mathematical Analysis and Applications} 334 (2007) 261-272.

\item Roshchina, V.:
Reducing Exhausters,
{\em Journal of Optimization Theory and Applications} 136 (2008) 261-273.

\item Roshchina, V.:
Exact Calculus of Fr\'{e}chet Subdifferentials for Hadamard Directionally Differentiable Functions,
{\em Nonlinear Analysis} 69 (2008) 1112-1124.

\item Schechter, M.: (E-Article)
More on Subgradient Duality,
{\em Journal of Mathematical Analysis and Applications} 71 (1979) 251-262.

\item Seeger, A.:
Limiting Behavior of the Approximate Second-Order Sundifferential of a Convex Function,
{\em Journal of Optimization Theory and Applications} 74 (1992) 527-544.

\item Shapiro, A.:
On Concepts of Directional Differentiability,
{\em Journal of Optimization Theory and Applications} 66 (1990) 477-487.

\item Singer, I.:
Abstract Subdifferentials and Some Characterization of Optimal Solutions,
{\em Journal of Optimization Theory and Applications} 57 (1988) 361-368.

\item Song, W.:
Weak Subdifferential of Set-Valued Mappings,
{\em Optimization} 52 (2003) 263-276.

\item Taa, A.:
$\epsilon$-Subdifferentials of Set-Valued Maps and $\epsilon$-Weak Pareto Optimality for Multiobjective Optimization,
{\em Mathematical Methods of Operations Research} 62 (2005) 187-209.

\item Thibault, L.:
On Subdifferentials of Optimal Value Functions,
{\em SIAM Journal on Control and Optimization} 29 (1991) 1019-1036.

\item Thibault, L.:
Sequential Subdifferential Calculus and Sequential Lagrange Multipliers,
{\em SIAM Journal on Control and Optimization} 35 (1997) 1434-1444.

\item Uderzo, A.:
Fr\'{e}chet Quasidifferential Calculus with Applications to Metric Regularity of Continuous Maps,
{\em Optimization} 54 (2005) 469-493.

\item Verona, A. and Verona, M.E.:
Remarks on Subgradients and $\epsilon$-Subgradients,
{\em Set-Valued Analysis} 1 (1993) 261-272.

\item Wang, G. and Wu, C.:
Directional Derivatives and Subdifferential of Convex Fuzzy Mappings and Application in Convex Fuzzy Programming,
{\em Fuzzy Sets and Systems} 138 (2003) 559-591.

\item Ward, D.E.:
A Chain Rule for First- and Second-Order Epiderivatives and Hypoderivatives,
{\em Journal of Mathematical Analysis and Applications} 348 (2008) 324-336.

\item Zagrodny, D.:
The Maximal Monotonicity of the Subdifferentials of Convex Functions: Simons’ Problem,
{\em Set-Valued Analysis} 4 (1996) 301-314.

\item Zhang, L.W. and Xia, Z.Q.:
Newton-Type Methods for Quasidifferentiable Equations,
{\em Journal of Optimization Theory and Applications} 108 (2001) 439-456.

\item Zowe, J. : (E-Articles and Print)
Subdifferentiability of Convex Functions with Values in an Ordered Vector Space,
{\em Mathematica Scandinava} 34 (1974) 69-83.

\begin{equation}{\label{d}}\tag{D}\mbox{}\end{equation}

Karush-Kuhn-Tucker Conditions.

\item Albert, M.:
Kuhn-Tucker Conditions and Linear Homogeneity,
{\em Economics Letters} 48 (1995) 267-272.

\item Bender, P.J.:
An Application of Guignard’s Generalized Kuhn-Tucker Conditions,
{\em Journal of Optimization Theory and Applications} 25 (1978) 585-589.

\item Birbil, S.I., Frenk, J.B.G. and Still, G.J.:
An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions
in Nonlinear Programming,
{\em European Journal of Operational Research} 180 (2007) 479-484.

\item Bonettini, S., Galligani, E. and Ruggiero, V.:
A Inexact Newton Method Combined with Hestenes Multipliers’ Scheme
for the Solution of Karush-Kuhn-Tucker Systems,
{\em Applied Mathematics and Computation} 168 (2005) 651-676.

\item Brezhneva, O.A., Tretyakov, A.A. and Wright, S.E.:
A Simple Elementary Proof of the Karush-Kuhn-Tucker Theorem
for Inequality-Constrained Optimization,
{\em Optimization Letters} 3 (2009) 7-10.

\item de la Fuente, A. and Naranjo, M.T.:
Continuity of the Constraint Correspondence in Parameterized Kuhn-Tucker Problems with Concave Constraints,
{\em Economics Letters} 62 (1999) 301-305.

\item Diamond, P. and Kloeden, P.:
Robust Kuhn-Tucker Conditions and Optimization Under Imprecision,
in Fuzzy Optimization, M. Delgado, J. Kacprzyk, J.-L. Verdegay and
M.A. Vila (eds) Physica-Verlag, Heidelberg, Germany, 61-66, 1994.

\item Dontchev, A.L. and Jongen, H.Th. :
On the Regularity of the Kuhn-Tucker Curve,
{\em SIAM J. Control Optimization} 24 (1986) 169-176.

\item Dunn, J.C. and Tian, T.:
Variants of the Kuhn-Tucker Sufficient Conditions in Cones
of Nonnegative Functions,
{\em SIAM J. Control and Optimization} 30 (1992) 1361-1384.

\item El Maghri, M. and Bernoussi, B.:
Pareto Optimizing and Kuhn-Tucker Stationary Sequences,
{\em Numerical Functional Analysis and Optimization} 28 (2007) 287-305.

\item Feng, G., Lin, Z. and Yu, B.:
Existence of an Interior Pathway to a Karush-Kuhn-Tucker Point
of a Nonconvex Programming Problem,
{\em Nonlinear Analysis, Theory, Methods \& Applications} 32 (1998) 761-768.

\item Giorgi, G., Jim\'{e}nez, B. and Novo, V.:
Strong Kuhn-Tucker Conditions and Constraint Qualifications in
Locally Lipschitz Multiobjective Optimization Problems,

\item Glover, B.M., Craven, B.D. and Flam, S.D.:
A Generalized Karush-Kuhn-Tucker Optimality COndition without
Constraint Qualification Using the Approximate Subdifferential,
{\em Numerical Functional Analysis and Optimization} 14 (1993) 333-353.

\item Guignard, M. :
Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in
a Banach Space,
{\em SIAM J. Control} 7 (1969) 232-241.

\item G\”{u}nzel, H.:
On the Topology of the Karush-Kuhn-Tucker Set under Mangasarian-Fromovitz
Constraint Qualification,
{\em SIAM Journal on Control and Optimization} 33 (1995) 1847-1856.

\item Haimes, Y.Y. and Chankong, V. :
Kuhn-Tucker Multipliers as Trade-offs in Multiobjective Decision-Making
Analysis.
{\em Automatica} 15 (1979) 59-72.

\item Hanson, M.A.:
On Sufficiency of the Kuhn-Tucker Conditions,
{\em Journal of Mathematical Analysis and Applications} 80 (1981) 545-550.

\item Hanson, M.A.:
Invexity and the Kuhn-Tucker Theorems,
{\em Journal of Mathematical Analysis and Applications} 236 (1999) 594-604.

\item Hirabayashi, R., Shida, M. and Shindoh, S.:
Manifold Structure of the Karush-Kuhn-Tucker Stationary Solution Set
with Two Paremeters,
{\em SIAM Journal on Optimization} 3 (1993) 564-581.

\item Izmailov, A.F. and Solodov, M.V.:
Karush-Kuhn-Tucker Systems: Regularity Conditions, Error Bounds and
a Class of Newton-Type Methods,
{\em Mathematical Programming}, Ser. A, 95 (2003) 631-650.

\item Izmailov, A.F. and Solodov, M.V.:
A Note on Solution Sensitivity for Karush-Kuhn-Tucker Systems,
{\em Mathematical Methods of Operations Research} 61 (2005) 347-363.

\item Jaffray, J.-Y. and Ch. Pomerol, J.:
A Direct Proof of the Kuhn-Tucker Necessary Optimality Theorem for
Convex and Affine Inequalities,
{\em SIAM Review} 31 (1989) 671-674.

\item Jeyakumar, V., Lee, G.M. and Srisatkunrajah, S.:
New Kuhn-Tucker Sufficiency for Global Optimality via Convexification,
{\em Nonlinear Analysis} 71 (2009) 373-381

\item Jeyakumar, V. and Srisatkunrajah, S.:
Geometric Conditions for Kuhn-Tucker Sufficiency of Global Optimality
in Mathematical Programming,
{\em European Journal of Operational Research} 194 (2009) 363-367.

\item Jeyakumar, V., Srisatkunrajah, S. and Huy, N.Q.:
Kuhn-Tucker Sufficiency for Global Minimum of Multi-Extremal
Mathematical Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 335 (2007) 779-788.

\item Kawasaki, H.:
Second-Order Necessary Conditions of the Kuhn-Tucker Type
under New Constraint Qualifications,
{\em Journal of Optimization Theory and Applications} 57 (1988) 253-264.

\item Kjeldsen, T.H.:
A Conceptualized Historical Analysis of the Kuhn-Tucker Theorem
in Nonlinear Theorem: The Impact of World War II,
{\em Historia Mathematica} 27 (2000) 331-361.

\item Kyparisis, J. :
On Uniqueness of Kuhn-Tucker Multipliers in Nonlinear Programming,
{\em Mathematical Programming} 32 (1985) 242-246.

\item Levine, P. and Pomerol, J.-Ch. :
Sufficient Conditions for Kuhn-Tucker Vectors in Convex Programming,
{\em SIAM J. Control and Optimization} 17 (1979) 689-699.

\item Li, X.F. and Zhang, J.Z.:
Stronger Kuhn-Tucker Type Conditions in Nonsmooth Multiobjective
Optimization: Locally Lipschitz Case,
{\em Journal of Optimization Theory and Applications} 127 (2005) 367-388.

\item Lv, Y., Hu, T., Wang, G. and Wan, Z.:
A Penalty Function Method Based on Kuhn-Tucker Condition for
Solving Linear Bilevel Programming,
{\em Applied Mathematics and Computation} 188 (2007) 808-813.

\item Mijangos, E. and Nabona, N.:
On the First-Order Estimation of Multipliers from Kuhn-Tucker Systems,
{\em Computers and Operations Research} 28 (2001) 243-270.

\item Mjelde, K.M.:
Sufficiency of Kuhn-Tucker Optimality Conditions for a Frational
Programming Problem,
{\em BIT} 18 (1978) 454-456.

\item Morgan, J. and Romaniello, M.:
Scalarization and Kuhn-Tucker-Like Conditions for Weak Vecor Generalized
Quasivariational Inequalities,
{\em Journal of Optimization Theory and Applications} 130 (2006) 309-316.

\item Nieuwenhuis, J.W. :
Another Application of Guignard’s Generalized Kuhn-Tucker Conditions,
{\em Journal of Optimization Theory and Applications} 30 (1980) 117-125.

\item Pang, J.-S.:
Serial and Parallel Computation of Karush-Kuhn-Tucker Points
via Nonsmooth Equations,
{\em SIAM J. Optimization} 4 (1994) 872-893.

\item Qi, H., Qi, L. and Sun, D.:
Solving Karush-Kuhn-Tucker Systems via the Trust Region and the
Conjugate Gradient Methods,
{\em SIAM Journal on Optimization} 14 (2003) 439-463.

\item Reiland, T.W. and Hanson, M.A. :
Generalized Kuhn-Tucker Conditions and Duality for Continuous Nonlinear
Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 74 (1980) 578-598.

\item Robinson, S.M. :
Perturbed Kuhn-Tucker Points and Rates of Convergence for a Class of
Nonlinear Programming Problems,
{\em Mathematical Programming} 7 (1974) 1-16.

\item Rockafellar, R.T. and Wets, R.J.-B. :
Stochastic Convex Programming : Kuhn-Tucker Conditions,
{\em J. Mathematical Economics} 2 (1975) 349-370.

\item Rupp, T. :
Kuhn-Tucker Curves for One-Parametric Semi-Infinite Programming,
{\em Optimization} 20 (1989) 61-77.

\item Shi, C., Lu, J. and Zhang, G.:
An Extended Kuhn-Tucker Approach for Linear Bilevel Programming,
{\em Applied Mathematics and Computation} 162 (2005) 51-63.

\item Simons, S.:
Abstract Kuhn-Tucker Theorems,
{\em Journal of Optimization Theory and Applications} 58 (1988) 147-152.

\item Tam, N.N. and Yen, N.D.:
Continuity Properties of the Karush-Kuhn-Tucker Point Set in
Quadratic Programming Problems,
{\em Mathematical Programming} 85 (1999) 193-206.

\item Tapia, R.A. and Trosset, M.W.:
An Extension of the Karush-Kuhn-Tucker Necessity Conditions to Infinite Programming,
{\em SIAM Review} 36 (1994) 1-17.

\item Travain, M.C.:
On Lagrange-Kuhn-Tucker Multipliers for Pareto Optimization Problems,
{\em Numerical Functional Analysis and Optimization} 15 (1994) 689-693.

\item Trudzik, L.I.:
Asymptotic Kuhn-Tucker Conditions in Abstract Spaces,
{\em Numerical Functional Analysis and Optimization} 4 (1982) 355-369.

\item V\'{a}zquez, F.G. and R\”{u}ckmann, J.-J.:
Extensions of the Kuhn-Tucker Constraint Qualification to Generalized
Semi-Infinite Programming,
{\em SIAM J. Optimization} 15 (2005) 926-937.

\item Wang, Y. and Zhang, L.:
Properties of Equation Reformulation of the Karush-Kuhn-Tucker
Condition for Nonlinear Second Order Cone Optimization Problems,
{\em Mathematical Methods of Operations Research}

\item Wierzbicki, A.P. :
Note on the Equivalence of Kuhn-Tucker Complementarity Conditions to an
Equation,
{\em Journal of Optimization Theory and Applications} 37 (1982) 401-405.

\item Xu, Q. and Yu, B.:
Solving the Karush-Kuhn-Tucker System of a Nonconvex Programming Problem
on an Unbounded Set,
{\em Nonlinear Analysis} 70 (2009) 757-763.

\item Zhang, Y., Xu, Y.-T. and Wang, F.:
Necessary and Sufficient Conditions for Kuhn-Tucker Type Optimality and for Weak Duality of Nonsmooth Programming,
{\em Nonlinear Analysis} 71 (2009) 4007-4011.

\item Zlobec, S. :
Asymptotic Kuhn-Tucker Conditions for Mathematical Programming Problems in
Banach Space,
{\em SIAM J. Control} 8 (1970) 505-512.

\item Zlobec, S. :
Extensions of Asymptotic Kuhn-Tucker Conditions in
Mathematical Programming,
{\em SIAM J. Appl. Math.} 21 (1971) 448-460.

\begin{equation}{\label{e}}\tag{E}\mbox{}\end{equation}

Optimality Conditions.

\item Achtziger, W. and Kanzow, C.:
Mathematical Programs with Vanishing Constraints: Optimality Conditions and Constraint Qualifications,
{\em Mathematical Programming}, Ser. A, 114 (2008) 69-99.

\item Arutyunov, A.V., Avakov, E.R. and Izmailov, A.F.:
Necessary Optimality Conditions for Constrained Optimization Problems under Relaxed Constraint Qualifications,
{\em Mathematical Programming, Ser A., 114 (2008) 37-68.

\item Bedna\v{r}\'{i}k, D. and Pastor, K.:
On Second-Order Conditions in Unconstrained Optimization,
{\em Mathematical Programming}, Ser. A, 113 (2008) 283-298.

\item Ben-Tal, A. and Zowe, J. :
Second Order Optimality Conditions for the $L_{1}$-Minimizatin Problem,
{\em Appl. MAth. Optim.} 13 (1985) 45-58.

\item Birbil, S.I., Frenk, J.B.G. and Still, G.J.:
An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions in Nonlinear Programming,
{\em European Journal of Operational Research} 180 (2007) 479-484.

\item Brinkhuis, J.:
A Linear Programming Proof of the Second Order Conditions of Nonlinear Programming,
{\em European Journal of Operational Research} 192 (2009) 1001-1007.

\item Castellani, M.:
A Dual Representation for Proper Positively Homogeneous Functions,
{\em Journal of Global Optimization} 16 (2000) 393-400.

\item Castellani, M.:
On Constraint Qualification in Nonlinear Programming,
{\em Nonlinear Analysis} 69 (2008) 3249-3258.

\item Dutta, J. and Lalitha, C.S.:(Vector Optimization)
Bounded Sets of KKT Multipliers in Vector Optimization,
{\em Journal of Global Optimization} 36 (2006) 425-437.

\item Guti\'{e}rrez, C., Jim\'{e}nez, B. and Novo, V.:
A Unified Approach and Optimality Conditions for Approximate Solutions of Vector Optimization Problems,
{\em SIAM Journal on Optimization} 17 (2006) 688-710.

\item Khanh, P.Q. and Tuan, N.D.:
First and Second-Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces,
{\em Journal of Optimization Theory and Applications} 130 (2006) 289-308.

\item Khanh, P.Q. and Tuan, N.D.:
Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadmard Directional Derivatives,
{\em Journal of Optimization Theory and Applications} 133 (2007) 341-357.

\item Linh, N.T.H. and Penot, J.-P.:
Optimality Conditions for Quasiconvex Programs,
{\em SIAM Journal on Optimization} 17 (2006) 500-510.

\item Liu, J.-C.:
Optimality and Duality for Generalized for Generalized Fractional Programming Involving Nonsmooth $(F,\rho )$-Convex Functions,
{\em Computers and Mathematics with Applications} 32 (1996) 91-102.

\item Maurer, H. and Zowe, J. :
First and Secong-Order Necessary and Sufficient Optimality Conditions for Infinite-Dimensional Programming Problems,
{\em Mathematical Programming} 16 (1979) 98-110.

\item Moeseke, P.V.:
Saddlepoint in Homogeneous Programming without Slater Condition,
{\em Econometrica} 42 (1974) 593-596.

\item Outrata, J.V. and R\”{o}misch, W.:
On Optimality Conditions for Some Nonsmooth Optimization Problems over $L^{p}$ Spaces,
{\em Journal of Optimization Theory and Applications} 126 (2005) 411-438.

\item Pastor, K.:
A Note on Second-Order Optimality Conditions,
{\em Nonlinear Analysis} 71 (2009) 1964-1969.

\item Penot, J.-P.:
Characterization of Solution Sets of Quasiconvex Programs,
{\em Journal of Optimization Theory and Applications} 117 (2003) 627-636.

\item Yang, X.Q. and Jeyakumar, V.:
First and Second-Order Optimality Conditions for Convex Composite Multiobjective Optimization,
{\em Journal of Optimization Theory and Applications} 95 (1997) 209-224.

\item Zalmai, G.J.:
Parameter-Free Sufficient Optimality Conditions and Duality Models for Minmax Fractional Subset Programming Problems with Generalized $({\cal F},\rho ,\theta )$-Convex Functions,
{\em Computers and Mathematics with Applications} 45 (2003) 1507-1535.

\begin{equation}{\label{f}}\tag{F}\mbox{}\end{equation}

Nonsmooth Optimization Problems.

\item Alber, Y.I., Iusem, A.N. and Solodov, M.V.:
Minimization of Nonsmooth Convex Functionals in Banach Spaces,
{\em Journal of Convex Analysis} 4 (1997) 235-255.

\item Alonso, M. and Rodriguez-Marin, L.:
Approximations of Nondifferentiable Functions and Local Topological Equivalence,
{\em Journal of Mathematical Analysis and Applications} 275 (2002) 771-788.

\item Ammar, E.E.:
On Some Basic Notions of Fuzzy Parametric Nonsmooth Multiobjective Nonlinear Fractional Programming Problems,
{\em Fuzzy Sets and Systems} 99 (1998) 291-301.

\item Bannert, T. :
A Trust Region Algorithm for Nonsmooth Optimization,
{\em Mathematical Programming} 67 (1994) 247-264.

\item Bector, C.R., Bhatia, D. and Jain, P. :
Generalized Concavity and Duality in Miltiobjective Nonsmooth Programming,
{\em Utilitas Mathematica} 43 (1993) 71-78.

\item Ben-Tal, A. and Zowe, J.:
Necessary and Sufficient Optimality Conditions for a Class of Nonsmooth Minimization Problems,
{\em Mathematical Programming} 24 (1982) 70-91.

\item Ben-Tal, A. and Zowe, J.:
Directional Derivatives in Nonsmooth Optimization,
{\em Journal of Optimization Theory and Applications} 47 (1985) 483-490.

\item Bhatia, D. and Aggarwal, S.:
Optimality and Duality for Multiobjective Nonsmooth Programming,
{\em European Journal of Operational Research} 57 (1992) 360-367.

\item Brand\'{a}o, A.J.V., Rojas-Medar, M.A. and Silva, G.N.:
Nonsmooth Continuous-Time Optimization Problems: Necessary Conditions,
{\em Computers and Mathematics with Applications} 41 (2001) 1477-1486.

\item Chan, W.L., Huang, L.R. and Ng, K.F. :
On Generalized Second-Order Derivatives and Taylor Expansions in Nonsmooth Optimization,
{\em SIAM J. Control and Optimization} 32 (1994) 591-611.

\item Chaney, R.W. :
Second-Order Sufficient Conditions for Nondifferentaible Programming Problems,
{\em SIAM J. Control and Optimization} 20 (1982) 20-33.

\item Chaney, R.W. :
Second-Order Necessary Conditions in Constrained Semismooth Optimization,
{\em SIAM J. Control and Optimization} 25 (1987) 1072-1081.

\item Chen, X. and Fukushima, M.:
Proximal Quasi-Newton Methods for Nondifferentiable Convex Optimization,
{\em Mathematical Programming} 85 (1999) 313-334.

\item Clarke, B.R. :
Nonsmooth Analysis and Fr\'{e}chet Differentiability of M-Functionals,
{\em Probability Theory and Related Fields} 73 (1986) 197-209.

\item Craven, B.D. and Yang, X.Q. :
A Nonsmooth Version of Alternative Theorem and Nonsmooth Multiobjective
Programming,
{\em Utilitas Mathematica} 40 (1991) 117-128.

\item El Abdouni, B. and Thibault, L. :
Lagrange Multipliers for Pareto Nonsmooth Programming Problems in Banach
Spaces,
{\em Optimization} 26 (1992) 277-285.

\item Elluia, R. and Hassouni, A.:
Characterization of Nonsmooth Functions through Their Generalized Gradients,
{\em Optimization} 22 (1991) 401-416.

\item Gaudioso, M. and Monaco, M.F. :
Variants to the Cutting Plane Approach for Convex Nondifferentiable Optimization,
{\em Optimization} 25 (1992) 65-75.

\item Ginchev, I.:
Higher Order Optimality Conditions in Nonsmooth Optimization,
{\em Optimization} 51 (2002) 47-72.

\item Henrion, R. and Jourani, A.:
Subdifferential Conditions for Calmness of Convex Cosntraints,
{\em SIAM Journal on Optimization} 13 (2002) 520-534.

\item Higle, J.L. and Sen, S. :
On the Convergence of Algorithms with Implications for Stochastic and
Nondifferentiable Optimization,
{\em Mathematics of Operations Research} 17 (1992) 112-131.

\item Huang, L.R. and Ng, K.F. :
Second-Order Necessary and Sufficient Conditions in Nonsmooth Optimization,
{\em Mathematical Programming} 66 (1994) 379-402.

\item Jeyakumar, V. :
A General Farkas Lemma and Characterization of Optimality for a Nonsmooth Program Involving Convex Process,
{\em Journal of Optimization Theory and Applications} 55 (1987) 449-461.

\item Jeyakumar, V. and Yang, X.Q. :
Convex Composite Multiobjective Nonsmooth Programming,
{\em Mathematical Programming} 59 (1993) 325-343.

\item Jiang, H. and Qi, L. :
A New Nonsmooth Equations Approach to Nonlinear Complementarity Problems,
{\em SIAM J. Control Optim} 35 (1997) 178-193.

\item Kannai, Y. and Tannenbaum, E.:
Paths Leading to the Nash Set for Nonsmooth Games,
{\em International Journal of Game Theory} 27 (1998) 393-405.

\item Kanniappan, P. :
Necessary Conditions for Optimality of Nondifferentiable Convex Multiobjective Programming,
{\em Journal of Optimization Theory and Applications} 40 (1983) 167-174.

\item Kanniappan, P. and Sastry, S.M.A. :
Duality Theorems and an Optimality Condition for Nondifferentiable Convex Programming,
{\em J. Austral. Math. Soc.} 32 (1982) 369-379.

\item Khanh, P.Q. and Tuan, N.D.:
Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadmard Directional Derivatives,
{\em Journal of Optimization Theory and Applications} 133 (2007) 341-357.

\item Khanh, P.Q. and Tuan, N.D.:
First and Second-Order Approximation as Derivatives of Mappings in Optimality Conditions for Nonsmooth Vector Optimization,
{\em Applied Mathematics and Optimization} 58 (2008) 147-166.

\item Kim, G.S., Kim, M.H. and Lee, G.M.:
On Optimality and Duality for Nonsmooth Multiobjective Fractional Optimization Problems,
{\em Nonlinear Analysis} 63 (2005) 1867-1876.

\item Kim, M.S., Choi, D.H. and Hwang, Y.:
Composite Nonsmooth Optimization Using Approximate Generalized Gradient Vectors,
{\em Journal of Optimization Theory and Applications} 112 (2002) 143-165.

\item Kim, S. and Um, B.-S. :
An Improved Subgradient Method for Constrained Nondifferentiable Optimization,
{\em Operations Reseach Letter} 14 (1993) 61-64.

\item King, A.J. and Rockafellar, R.T. :
Sensitivity Analysis for Nonsmooth Generalized Equations,
{\em Mathematical Programming} 55 (1992) 193-212.

\item Kiwiel, K.C.:
Descent Methods for Quasidifferentiable Minimization,
{\em Applied Mathematics and Optimization} 18 (1988) 163-180.

\item Kiwiel, K.C.:
A Bundle Bregman Proximal Method for Convex Nondifferentiable Minimization,
{\em Mathematical Programming} 85 (1999) 241-258.

\item Lai, H.-C, and Ho, C.P. :
Duality Theorem of Nondifferentiable Convex Multiobjective Programming.
{\em Journal of Optimization Theoey and Applications} 50 (1986) 407-420.

\item Lai, H-.C. and Huang, T.Y.:
Optimality Conditions for a Nondifferentiable Minimax Programming in Complex Spaces,
{\em Nonlinear Analysis} 71 (2009) 1205-1212.

\item Lal, S.N., Nath, B. and Kumar, A. :
Duality for Some Nondifferentiable Static Multiobjective Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 186 (1994) 862-867.

\item Li, X.F.:
Constraint Qualifications in Nonsmooth Multiobjective Optimization,
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Stronger Kuhn-Tucker Type Conditions in Nonsmooth Multiobjective Optimization: Locally Lipschitz Case,
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\item Liu, J.C. :
Optimality and Duality for Generalized Fractional Programming Involving Nonsmooth Pseudoinvex Functions,
{\em Journal of Mathematical Analysis and Applications} 202 (1996) 667-685.

\item Liu, J.C.:
$\epsilon$-Pareto Optimality for Nondifferentiable Multiobjective Programming via Penalty Function,
{\em Journal of Mathematical Analysis and Applications} 198 (1996) 248-261.

\item Liu, J.-C.:
Optimality and Duality for Generalized for Generalized Fractional Programming Involving Nonsmooth $(F,\rho )$-Convex Functions,
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Semismooth and Semiconvex Functions in Constrained Optimization,
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Newton Methods for Nonsmooth Convex Minimization: Connections among ${\cal U}$-Lagrangian, Riemannian, Newton and SQP Metods,
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A Class of Nondifferentiable Mathematical Programming Problems,
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Duality for a Class of Nondifferentiable Multiobjective Programs,
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\item Mond, B. and Schechter, M. :
On a Constraint Dualification in a Nondifferentiable Programming Problem,
{\em Naval Res. Log. Quart.} 23 (1976) 611-613.

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Duality for Nondifferentiable Programming without a Constraint Qualification,
{\em Utilitas Mathematica} 15 (1979) 291-302.

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Generalized Differential Calculus for Nonsmooth and Set-Valued Mappings,
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Generalized $(F,\rho )$-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization,
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Optimality Criteria for Nonsmooth Continuous-Time Problems of Multiobjective Optimization,
{\em Journal of Optimization Theory and Applications} 136 (2008) 69-76.

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Duality for Nonsmooth Continuous-Time Problems of Vector Optimization,
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Serial and Parallel Computation of Karush-Kuhn-Tucker Points
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A Necessary Optimality Condition for Nondifferentiable Constrained Extremum Problems,
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Softness, Sleekness and Regularity Properties in Nonsmooth Analysis,
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Nonsmooth Continuous-Time Optimization Problems: Sufficient Conditions,
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Generalized Convexity and Nonsmooth Problems of Vector Optimization,
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An Interval Algorithm for Nondifferentiable Global Optimization,
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Nonsmooth Multiple-Objective Optimization in Separable Hilbert Spaces,
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$\epsilon$-Optimal Solutions in Nondifferentiable Convex Programming and Some Related Questions,
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Generalized Nonsmooth Invexity over Cone in Vector Optimization,
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Constraint Qualifications in a Class of Nondifferentiable Mathematical Programming,
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Optimization with Nonsmooth Data,
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\begin{equation}{\label{g}}\tag{G}\mbox{}\end{equation}

Numerical Methods for Optimization Problems.

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Projected Gradient Methods for Linearly Constrained Problems,
{\em Mathematical Programming} 39 (1987) 93-116.

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A Modified Newton Method for Minimization,
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Newton-Type Methods for Unconstrained and Linearly Constrained Optimization,
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A Newton Method for Linear Programming,
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A Superlinearly Convergent Method for Minimization Problems with Linear Inequality Constraints,
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\begin{equation}{\label{h}}\tag{H}\mbox{}\end{equation}

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Generalized Invexity and Duality in Multiobjective Programming Problems,
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Symmetric Duality for Multiobjective Fractional Variational Problems
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{\em European Journal of Operational Research} 188 (2008) 695-704.

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On Optimality and Duality Theorems of Nonlinear Disjunctive Fractional
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A Review of Duality Theory for Linear Programming over Topological Vector
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Duality and Algorithm for a Class of Continuous Transportation Problems,
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Dual Problems and Separation of Sets : Lagrange and Fenchel Duality,
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Duality Theory and Slackness Conditions in Multiobjective Linear Programming,
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Duality Theory of Linear Programs : A Constructive Approach with
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On Symmetric Duality in Nonlinear Programming,
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Strong Duality in Nonconvex Quadartic Optimization with Two Quadratic
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Wolfe-Type Duality Invloving $(B,\eta )$-Invex Functions for a Minimax
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Generalized Concavity and Duality in Miltiobjective Nonsmooth Programming,
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Optimality Conditions and Duality in Subdifferentiable Multiobjective
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A Linearization Approach to Multiobjective Programming Duality,
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Asymptotic Duality over Closed Convex Sets,
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Duality for Nonlinear Multiple-Criteria Optimization Problems.
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A Strong Duality Theorem for the Minimum of a Family of Convex Programs,
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A D-induced Duality and Its Applications,
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Duality for Multiple Objective Convex Programs,
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Adjoint Process Duality,
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Strong Duality for Generalized Convex Optimization Problems,
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Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory,
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A Note on Pseudo-Invexity and Duality in Nonlinear Programming,
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Technical Note on Symmetric Duality in Multiobjective Programming: Some Remarks on Recent Results,
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Duality in Semi-Infinite Programs and Some Works of Haar and Carath\'{e}odory,
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Dual Gradient Method for Linearly Constrained, Strongly Convex, Separable
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\item Cooper, W.W., Lelas, V. and Sueyoshi, T.:
Goal Programming Models and Their Duality Relations for Use in Evaluating
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Existence and Lagrangian Duality for Maximizations of Set-Valued Functions,
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Strong Vector Minimization and Duality,
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Invex Functions and Duality,
{\em Journal of Australian Math. Soc.} Ser. A, 39 (1985) 1-20.

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Alternative and Duality Theorems with Weakened Convexity,
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Symmetric Dual Multiobjective Programming,
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Symmetric Duality for Nonlinear Programming Problem Involving $\eta$-bonvex
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Self-Dual Quadratic Programs,
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An Infinite Linear Program with a Duality Gap,
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Asymptotic Cones and Duality of Linear Relations,
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Using Duality to Solve Discrete Optimization Problems : Theory and
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Duality Theorems for Certain Programs Involving Minimum or Maximum Operations,
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Additively Separable Duality Theory,
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Duality in Nonlinear Programming : A Simplified Applications-Oriented Development,
{\em SIAM Review} 13 (1971) 1-37.

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Quasi-Relative Interior-Type Constraint Qualifications Ensuring Strong Lagrange Duality for Optimization Problems with Cone and Affine Constraints,
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Subdifferentiability and the Duality Gap,
{\em Positivity} 6 (2002) 261-274.

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Symmetric Duality for Continuous Linear Programs,
{\em SIAM J Appl. Math.} 18 (1970) 84-97.

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Generalization of Fenchel’s Duality Theorem for Convex Vector Optimization,
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Nonconvex Dualization in Multiobjetive Optimization,
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Second Order Symmetric Duality for Nonlinear Minimax Mixed Integer Programs,
{\em European Journal of Operational Research} 101 (1997) 122-129.

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Duality and Self-Duality in Mathematical Programming,
{\em SIAM J. Appl. Math.} 12 (1964) 446-449.

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Duality for a Class of Infinite Programming Problems,
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Perfext Duality for Convexlike Programs,
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Duality and Statistical Tests of Optimality for Two Stage Stochastic Programs,
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On Some Relations between a Dual Pair of Multiple Objective Linear Programs,
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Duality in Vector Optimization,
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Asymptotic Dual Conditions Characterizing Optimality for Infinite Convex Programs,
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Constraint Qualifications Characterizing Lagrangian Duality in Convex Optimization,
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Complete Characterizations of Stable Farkas’ Lemma and Cone-Convex Programming Duality,
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Zero Duality Gaps in Infinite-Dimensional Programming,
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Duality Theorems and an Optimality Condition for Nondifferentiable Convex Programming,
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Duality Gaps in Semi-Infinite Linear Programming – An Approxination Problem,
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Optimality Criteria and Duality in Multiple-Objective Optimization Involving Generalized Invexity,
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A Duality in Multiobjective Nonlinear Programming,
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Non-Differentiable Symmetric Duality for Multiobjective Programming with
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Multiobjective Symmetric Duality with Cone Constraints,
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Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming,
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Strong Duality for Infinite-Dimentional Vector-Valued Programming Problems,
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Saddle Point and Duality in the Optimization Theory of Convex Set Functiuons.
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Duality Theorem of Nondifferentiable Convex Multiobjective Programming,
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Duality for Some Nondifferentiable Static Multiobjective Programming Problems,
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Infinite Programming and Duality in Topological Vector Spaces,
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\item Li, Z.-F.:
Lagrangian Multipliers, Saddle Points, and Duality in Vector Optimization of Set-Valued Maps,
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Optimality and Duality for Generalized Fractional Programming Involving
Nonsmooth Pseudoinvex Functions,
{\em J. Math. Anal. Appl.} 202 (1996) 667-685.

\item Liu, J.-C.:
Optimality and Duality for Generalized for Generalized Fractional
Programming Involving Nonsmooth $(F,\rho )$-Convex Functions,
{\em Computers and Mathematics with Applications} 32 (1996) 91-102.

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Three Types Dual Model for Minimax Fractional Programming,
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$\varepsilon$-Optimality and Duality for Multiobjective Fractional
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{\em Computers and Mathematics with Applications} 37 (1999) 119-128.

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Duality of Fuzzy ${\mbox MC}^{2}$ Linear Programming : A Constructive
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{\em J. Math. Anal. Appl.} 194 (1995) 389-413.

\item Luc, D.T., Phong, T.Q. and Volle, M.:
A New Duality Approach to Solving Concave Vector Maximization Problems,
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Fenchel and Lagrange Duality are Equivalent,
{\em Methamatical Programming} 7 (1974) 253-258.

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Duality and Reciprocity for Vector Programming,
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Duality Theorems and Theorems of the Alternative,
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Symmetric Duality for Structured Convex Programs,
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Optimality Conditions and Strong Duality in Abstract and Continuous-Time
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Multiobjective Second Order Symmetric Duality with Cone Constraints,
{\em European Journal of Operational Research} 126 (2000) 675-682.

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Non-Differentiable Higher-Order Symmetric Duality in Methematical Programming
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{\em European Journal of Operational Research} 167 (2005) 28-34.

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Mond-Weir Type Second Order Symmetric Duality in Non-differentiable Minimax
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{\em European Journal of Operational Research} 170 (2006) 355-362.

\item Mishra, S.K., Giorgi, G. and Wang, S.Y.:
Duality in Vector Optimization in Banach Spaces with Generalized Convexity,
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\item Mishra, S.K., Wang, S.Y. and Lai, K.K.:
Optimality and Duality for a Multi-Objective Programming Problem Involving
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Duality for a Class of Nondifferentiable Multiobjective Programs,
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\item Mond, B. \& Schechter, M. :
On a Constraint Dualification in a Nondifferentiable Programming Problem,
{\em Naval Res. Log. Quart.} 23 (1976) 611-613.

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Duality for Nondifferentiable Programming without a Constraint Qualification,
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Symmetric Duality with Pseudo-Invexity in Variational Problems,
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Sufficient Conditions for Duality Theorems in Infinite Linear Programming
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Geometric Consideration of Duality in Vector Optimization.
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Sufficiency Conditions and a Duality Theory for Mathematical Programming
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Johri’s General Dual, the Langragian Dual, and the Surrogate Dual,
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Conjugate Functions for Convex and Nonconvex Duality,
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Duality for a Class of Quasiconvex Programs,
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Are Dualities Appropriate for Duality Theories in Optimization?,
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Symmetric Duality for Generalized Unconstrained Geometric Programming,
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A Simple Duality Proof in Convex Quadratic Programming with a Quadratic
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On Efficiency and Duality for Multiobjective Programs,
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Optimality Conditions and Duality in Continuous Programming I. Convex
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Optimality Conditions and Duality in Continuous Programming II. The Linear
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Generalized Kuhn-Tucker Conditions and Duality for Continuous Nonlinear
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Some Duality Theorems for the Non-linear Vector Maximum Problem,
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Duality for Nonlinear Programming in a Banach Space,
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Duality Theorems for Convex Functions,
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Extension of Fenchel’s Duality Theorem for Convex Functions,
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Duality and Stability in Extremum Problems Involving Convex Functions,
{\em Pacific J. Math} 21 (1967) 167-187.

\item Rockafellar, R.T. :
Duality in Nonlinear Programming,
in “American Mathematical Society Lectures in Applied Mathematics”, Vol II
(Dantzig, G. \& Veinott, A., Eds) pp. 401-422, 1968.

\item Rockafellar, R.T. :
Some Convex Programs Whose Duals are Linearly Constrained,
{\em Nonlinear Programming}, Rosen, J.B. et al., (eds) Academic Press,
NY, 1970, pp.293-322.

\item Rockafellar, R.T. :
Existence and Duality Theorems for Convex Problems of Bolza,
{\em Trans. Amer. Math. Soc.} 159 (1971) 1-40.

\item Rockafellar, R.T. :
A Dual Approach to Solving Nonlinear Programming Problems by Unconstrained
Optimization,
{\em Mathematical Programming} 5 (1973) 354-373.

\item Rockafellar, R.T. :
Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming,
{\em SIAM J. Control} 12 (1974) 268-285.

\item Rockafellar, R.T. :
Dualization of Subgradient Conditions for Optimality,
{\em Nonlinear Analysis} 20 (1993) 627-646.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
A Dual Strategy for the Implementation of the Aggregation Principle in
Decision Making under Uncertainty,
{\em Applied Statistic Models and Data Analysis} 8 (1992) 245-255.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
A Dual Solution Procedure for Quadratic Stochastic Programs with Simple
Recourse,
{\em Lecture Notes in Math.} 1005 (????) 252-265.

\item R\”{o}dder, W. \& Zimmermann, H.-J. :
Duality in Fuzzy Linear Programming,
{\em Internat. Symp. on Extremal Methods and Systems Analysis}, University
of Texas at Austin, 1977, pp.415-427.

\item Romeijn, H.E., Smith, R.L. \& Bean, J.C. :
Duality in Infinite Dimensional Linear Programming,
{\em Mathematical Programming} 53 (1992) 72-97.

\item Rosinger, E.E. :
Duality and Alternative in Multiobjective Optimization,
{\em Proc. Amer. Math. Soc.} 64 (1977) 307-312.

\item Sach, P.H. \& Craven, B.D. :
Invex Multifunctions and Duality,
{\em Numer. Funct. Anal. and Optim.} 12 (1991) 575-591.

\item Schechter, M. :
Duality in Continuous Linear Programming,
{\em J. Math. Anal. Appl.} 37 (1972) 130-141.

\item Schechter, M. :
A Subgradient Duality Theorem,
{\em J. Math. Anal. Appl.} 61 (1977) 850-855.

\item Schechter, M. :
Sufficient Conditions for Duality in Homogeneous Programming,
{\em J. Optimization Theory and Applications} 23 (1977) 389-400.

\item Schechter, M. :
More on Subgradient Duality,
{\em J. Math. Anal. Appl.} 71 (1979) 251-262.

\item Schurr, S.P., Tits, A.L. and O’Leary, D.P.:
Universal Duality in Conic Convex Optimization,
{\em Mathematical Programming}, Ser. A, 109 (2007) 69-88.

\item Singh, C., Bhatia, D. \& Rueda, N. :
Duality in Nonlinear Multiobjective Programming Using Augmented Lagragian
Functions,
{\em J. Optimization Theory and Applications} 88 (1996) 659-670.

\item Sinha, S.M. :
A Duality Theorem for Nonlinear Programming with a Duality Gap,
{\em Management Science} 12 (1965) 385-390.

\item Song, W.:
Duality for Vector Optimization of Set-Valued Functions,
{\em Journal of Mathematical Analysis and Applications} 201 (1996) 212-225.

\item Song, W. :
Conjugate Duality in Set-Valued Vector Optimization,
{\em Journal of Mathematical Analysis and Applications} 216 (1997) 265-283.

\item Song, W. :
Lagrangian Duality for Minimization of Nonconvex Multifunctions,
{\em J. Optimization Theory and Applications} 93 (1997) 167-182.

\item Stancu-Minasian, I.M.:
Optimality and Duality in Nonlinear Programming Involving Semilocally
B-Preinvex and Related Functions,
{\em European Journal of Operational Research} 173 (2006) 47-58.

\item Suneja, S.K., Aggarwal, S. and Davar, S.:
Multiobjective Symmetric Duality Involving Cones,
{\em European Journal of Operational Research} 141 (2002) 471-479.

\item Suneja, S.K., Lalitha, C.S. and Khurana, S.:
Second Order Symmetric Duality in Multiobjective Programming,
{\em European Journal of Operational Research} 144 (2003) 492-500.

\item Tammer, Ch. \& Tammer, K. :
Generalization and Sharpening of Some Duality Relations for a Class of
Vector Optimization Problems,
{\em ZOR} 35 (1991) 249-265.

\item Tanino, T.:
Conjugate Duality in Vector Optimization,
{\em Journal of Mathematical Analysis and Applications} 167 (1992) 84-97.

\item Tanino, T. and Sawaragi, Y. :
Duality Theory in Multiobjective Programming.
{\em Journal of Optimization Theory and Applications} 27 (1979) 509-529.

\item Tanino, T. \& Sawaragi, Y. :
Conjugate Maps and Duality in Multiobjective Optimization,
{\em J. Optimization Theory and Applications} 27 (1980) 473-499.

\item Tarvainen, K. :
Duality Theory for Preferences in Multiobjective Decisionmaking,
{\em J. Optimization Theory and Applications} 88 (1996) 237-245.

\item Thach, P.T., Konno, H. \& Yokota, D. :
Dual Approach to Minimization on the Set of Pareto-Optimal Solutions,
{\em J. Optimization Theory and Applications} 88 (1996) 689-707.

\item Tind, J. \& Wolsey, L.A. :
An Elementary Survey of General Duality Theory in Mathematical Programming,
{\em Mathematical Programming} 21 (1981) 241-261.

\item Tyndall, W.F. :
An Extended Duality Theorem for Continuous Linera Programming Problems,
{\em SIAM J. Appl. Math.} 15 (1967) 1294-1298.

\item Tyndall, W.F. :
A Duality Theorem for a Class of Continuous Linera Programming Problems,
{\em SIAM J. Appl. Math.} 15 (1965) 644-666.

\item Van Slyke, R.M. \& Wets, R. J.-B. :
A Duality Theory for Abstract Mathematical Programs with Applications to
Optimal Control Theory,
{\em J. Math. Anal. Appl.} 22 (1968) 679-706.

\item Wang, C.Y., Yang, X.Q. and Yang, X.M.:
Nonlinear Lagrange Duality Theorems and Penalty Function Methods
in Continuous Optimization,
{\em Journal of Global Optimization} 27 (2003) 473-484.

\item Wang, S. \& Li, Z. :
Scalarization and Lagrange Duality in Multiobjective Optimization,
{\em Optimization} 26 (1992) 315-324.

\item Wanka, G. :
On Duality in the Vectorial Control-Approximation Problem,
{\em ZOR} 35 (1991) 309-320.

\item Wolfe, P. :
A Duality Theorem for Nonlinear Programming,
{\em Quarterly of Applied Mathematics} 19 (1961) 239-244.

\item Wolsey, L.A. :
Integer Programming Duality : Price Functions and Sensitivity Analysis,
{\em Mathematical Programming} 20 (1981) 173-195.

\item Yang, X.M., Yang, X.Q. and Teo, K.L.:
Non-Differentiable Second Order Symmetric Duality in Mathematical
Programming with F-Convexity,
{\em European Journal of Operational Research} 144 (2003) 554-559.

\item Yang, X.M., Yang, X.Q. and Teo, K.L.:
Converse Duality in Nonlinear Programming with Cone Constraints,
{\em European Journal of Operational Research} 170 (2006) 350-354.

\item Zalmai, G.J. :
Duality for Generalized Fractional Programs Involving n-Set Functions,
{\em J. Math. Anal. Appl.} 149 (1990) 339-350.

\item Zalmai, G.J. :
Optimality Conditions and Duality for a Class of Continuous-Time Generalized
Fractional Programming Problems,
{\em J. Math. Anal. Appl.} 153 (1990) 356-371.

\item Zowe, J. :
A Duality Theorem for a Convex Programming Problem in Order Complete Vector
Lattices,
{\em J. Math. Anal. Appl.} 50 (1975) 273-287.

\begin{equation}{\label{i}}\tag{I}\mbox{}\end{equation}

Parametric Programming.

\item Brosowski, B. :
A Refinement of an Optimality Criterion and Its Application to Parametric
Programming,
{\em J. Optimization Theory and Applications} 42 (1984) 367-382.

\item Chern, M.-S., Jan, R.-H. \& Chern, R.-J. :
Parametric Nonlinaer Integer Programming : The Right-Hand Side Case,
{\em European J. Operational Research} 54 (1991) 237-255.

\item Fiacco, A.V. :
Computable Bounds on Parametric Solutions of Convex Problems,
{\em Mathematical Programming} 40 (1988) 213-221.

\item Gfrerer, H., Guddat, J. \& Wacker, Hj. :
A Globally Convergent Algorithm Based on Imbedding and Parametric Optimization,
{\em Computing} 30 (1983) 225-252.

\item Gollmer, R. :
On Linear Multiparametric Optimization with Parameter-Dependent Constraint
Matrix,
{\em Optimization} 16 (1985) 15-28.

\item Jongen, H.Th., Tonker, P. \& Twilt, F. :
One-Parameter Families of Optimization Problems : Equality Constraints,
{\em J. Optimization Theory and Applications} 48 (1986) 141-161.

\item Kojima, M. :
A Complementarity Pivoting Approach to Parametric Nonlinear Programming,
{\em Mathematics of Operations Research} 4 (1979) 464-477.

\item Kuk, H. :
Sensitivity Analysis in Parametrized Convex Vector Optimization,
{\em J. Math. Anal. Appl.} 202 (1996) 511-522.

\item Martin, D.H. :
On the Continuity of the Maximum in Parametric Linear Programming.
{\em Journal of Optimization Theory and Applications} 17 (1975) 205-210.

\item Murty, K.G. :
Computational Complexity of Parametric Linear Programming.
{\em Mathematical Programming} 19 (1980) 213-219.

\item Nakayama, H. :
Trade-off Analysis Using Parametric Optimization Techniques.
{\em European Journal of Operations Research} 60 (1992) 87-98.

\item Ritter, K. :
A Method for Solving Nonlinear Maximum Problems Depending on Parameters,
{\em Naval Res. Logist. Quart.} 14 (1967) 147-162.

\item Rupp, T. :
Kuhn-Tucker Curves for One-Parametric Semi-Infinite Programming,
{\em Optimization} 20 (1989) 61-77.

\item V\”{a}liaho, H. :
A Unified Approach to One-Parametric General Quadratic Programming,
{\em Mathematical Programming} 33 (1985) 318-338.

\begin{equation}{\label{j}}\tag{J}\mbox{}\end{equation}

Large-Scale Optimization.

\item Al-Jeiroudi, G., Gondzio, J. and Hall, J.:
Preconditioning Indefinite Systems in Interior Point Methods for Large Scale Linear Optimization,
{\em Optimization Methods and Software} 23 (2008) 345-363.

\item Benichou, M., Gauthier, J.M., Hentges, G. and Ribiere, G.:
The Efficient Solution of Large-Scale Linear Programming Problems — Some Algorithmic Techniques and Computational Results,
{\em Mathematical Programming} 13 (1977) 280-322.

\item Ben-Ameur, W. and Neto, J.:
A Constraint Generation Algorithm for Large-Scale Linear Programming Using Multiple-Points Separation,
{\em Mathematical Programming}, Ser. A 107 (2006) 517-537.

\item Bixby, R.E., Gregory, J.W., Lustig, I.J., Marsten, R.E. and Shanno, D.F.:
Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods,
{\em Operations Research} 40 (1992) 885-897.

\item Eldersveld, S.K. and Saunders, M.A.:
A Block-LU Update for Large-Scale Linear Programming,
{\em SIAM J. Matrix Anal. Appl.} 13 (1992) 191-201.

\item Evtushenko, Y.G., Golikov, A.I. and Mollaverdy, N.:
Augmented Lagrangian Method for Large-Scale Linear Programming Problems,
{\em Optimization Methods and Software} 20 (2005) 515-524.

\item Forsgren, A. and Murray, W.:
Newton Methods for Large-Scale Linear Equality-Constrained Minimization,
{\em SIAM J. Matrix Anal. Appl.} 14 (1993) 560-587.

\item Forsgren, A. and Murray, W.:
Newton Methods for Large-Scale Linear Inequality-Constrained Minimization,
{\em SIAM J. Optimization} 7 (1997) 162-176.

\item Graves, G.W. and McBride, R.D.:
The Factorization Approach to Large-Scale Linear Programming,
{\em Mathematical Programming} 10 (1976) 91-110.

\item Grinold, R.C.:
Steepest Ascent for Large Scale Linear Programs,
{\em SIAM Review} 14 (1972) 447-464.

\item Ioslovich, I.:
Robust Reduction of a Class of Large-Scale Linear Programs,
{\em SIAM J. Optimization} 12 (2001) 262-282.

\item Karmarkar, N.K. and Ramakrishnan, K.G.: (Large-Scale Optimization)
Computational Results of an Interior Point Algorithm for Large Scale Linear Programming,
{\em Mathematical Programming} 52 (1991) 555-586.

\item Murtagh, B.A. and Saunders, M.A.:
Large-Scale Linear Constrained Optimization,
{\em Mathematical Programming} 14 (1978) 41-72.

\item Oliveira, A.R.L. and Sorensen, D.C.:
A New Class of Preconditioners for Large-Scale Linear Systems from Interior Point Methods for Linear Programming,
{\em Linear Algebra and Its Applications} 394 (2005) 1-24.

\item Todd, M.J.:
Large-Scale Linear Programming: Geometry, Working Bases and Factorizations,
{\em Mathematical Programming} 26 (1983) 1-20.

\item Tseng, P.:
Relaxation Method for Large Scale Linear Programming Using Decomposition,
{\em Mathematics of Operations Research} 16 (1991) 859-880.

\item Wagner, M., Meller, J. and Elber, R.:
Large-Scale Linear Programming Techniques for the Design of Protein Folding Potentials,
{\em Mathematical Programming}, Ser. B 101 (2004) 301-318.

\item Zhao, G.Y.:
Interior-Point Methods with Decomposition for Solving Large-Scale Linear Programs,
{\em Journal of Optimization Theory and Applications} 102 (1999) 169-192.

\begin{equation}{\label{k}}\tag{K}\mbox{}\end{equation}

Fractional Programming.

\item Ammar, E.E.:
On Optimality and Duality Theorems of Nonlinear Disjunctive Fractional
Minmax Programs,
{\em European Journal of Operational Research} 180 (2007) 971-982.

\item Bector, C.R., Chandra, S. and Bector, M.K.:
Generalized Fractional Programming Duality: A Parametric Approach,
{\em Journal of Optimization Theory and Applications} 60 (1989) 243-260.

\item Bector, C.R., Chandra, S. and Husain, I. :
Optimality Conditions and Duality in Subdifferentiable Multiobjective
Frational Programming,
{\em Journal of Optimization Theory and Applications} 79 (1993) 105-125.

\item Benson, H.P.:
Fractional Programming with Convex Quadratic Forms and Functions,
{\em European Journal of Operational Research} 173 (2006) 351-369.

\item Bernard, J.C. and Ferland, J.A.:
Convergence of Intervla-Type Algorithms for Generalized Frational Programming,
{\em Mathematical Programming} 43 (1989) 349-363.

\item Boncompte, M. and Mart\'{i}nez-Legaz, J.E.:
Fractional Programming by Lower Subdifferentiability Techniques,
{\em Journal of Optimization Theory and Applications} 68 (1991) 95-116.

\item Crouzeix, J.P. and Ferland, J.A.:
Algorithms for Generalized Frational Programming,
{\em Mathematical Programming} 52 (1991) 191-207.

\item Crouzeix, J.P., Ferland, J.A. and Schiable, S.:
Duality in Generalized Linear Frational Programming,
{\em Mathematical Programming} 27 (1983) 342-354.

\item Crouzeix, J.P., Ferland, J.A. and Schiable, S.:
An Algorithm for Generalized Frational Programs,
{\em Journal of Optimization Theory and Applications} 47 (1985) 35-49.

\item Ferland, J.A.:
Generalized Fractional Programming: Algorithms and Numerical Experimentation,
{\em European Journal of Operational Research} 20 (1985) 92-101.

\item Flachs, J.:
Generalized Cheney-Loeb-Dinkelbach-Type Algorithms,
{\em Mathematics of Operations Research} 10 (1985) 674-687.

\item Husain, I. and Jabben, Z.:
Continuous-Time Fractional Minmax Programming,
{\em Mathematical and Computer Modelling} 42 (2005) 701-710.

\item Jagannathan, R.:
An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear
Fractional Objectives,
{\em Management Sciences} 31 (1985) 847-851.

\item Jagannathan, R. and Schaible, S.:
Duality in Generalized Frational Programming via Farkas’ Lemma,
{\em Journal of Optimization Theory and Applications} 41 (1983) 417-424.

\item Kim, G.S., Kim, M.H. and Lee, G.M.:
On Optimality and Duality for Nonsmooth Multiobjective Fractional
Optimization Problems,
{\em Nonlinear Analysis} 63 (2005) 1867-1876.

\item Liu, J.C. :
Optimality and Duality for Generalized Fractional Programming Involving
Nonsmooth Pseudoinvex Functions,
{\em J. Math. Anal. Appl.} 202 (1996) 667-685.

\item Liu, J.-C.:
Optimality and Duality for Generalized for Generalized Fractional
Programming Involving Nonsmooth $(F,\rho )$-Convex Functions,
{\em Computers and Mathematics with Applications} 32 (1996) 91-102.

\item Liu, J.-C., Kimura, Y. and Tanaka, K.:
Three Types Dual Model for Minimax Fractional Programming,
{\e, Computers and Mathematcis with Applications} 38 (1999) 143-155.

\item Liu, J.-C. and Yokoyama, K.:
$\varepsilon$-Optimality and Duality for Multiobjective Fractional
Programming,
{\em Computers and Mathematics with Applications} 37 (1999) 119-128.

\item Mishra, S.K., Pant, R.P. and Rautela, J.S.:
Generalized $\alpha$-Univexity and Duality for Nondifferentiable Minimax Fractional Programming,
{\em Nonlinear Analysis} 70 (2009) 144-158.

\item Mjelde, K.M.:
Sufficiency of Kuhn-Tucker Optimality Conditions for a Frational Programming Problem,
{\em BIT} 18 (1978) 454-456.

\item Scott, C.H. and Jefferson, T.R.: ()
Conjugate Duality in Generalized Fractional Programming,
{\em Journal of Optimization Theory and Applications} 60 (1989) 475-483.

\item Singh, C.:
A Class of Multiple-Criteria Fractional Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 115 (1986) 202-213.

\item Singh, C. and Rueda, N.:
Generalized Fractional Programming: Optimality and Duality Theory,
{\em Journal of Optimization Theory and Applications} 66 (1990) 149-159.

\item Yano, H. and Sakawa, M. :
Interactive Fuzzy Decision Making for Generalized Multiobjective Linear
Frational Programming Problems with Fuzzy Parameters,
{\em Fuzzy Sets and Systems} 32 (1989) 245-261.

\item Zalmai, G.J.:
Parameter-Free Sufficient Optimality Conditions and Duality Models for
Minmax Fractional Subset Programming Problems with Generalized
$({\cal F},\rho ,\theta )$-Convex Functions,
{\em Computers and Mathematics with Applications} 45 (2003) 1507-1535.

\begin{equation}{\label{l}}\tag{L}\mbox{}\end{equation}

Goal Programming.

\item Arenas Parra M., Bilbao Terol, A. and Rodr\'{i}guez Ur\'{i}a, M.V.: (E-Articles)
A Fuzzy Goal Programming Approach to Portfoilo Slection,
{\em European Journal of Operational Research} 133 (2001) 287-297.

\item Bhattacharya, U.K.: (E-Articles)
A Chance Constraints Goal Programming Model for the Advertising Planning Problem.
{\em European Journal of Operational Research} 192 (2009) 382-395.

\item Blake, J.T. and Carter, M.W.: (Goal Programming)(E-Articles)
A Goal Programming Approach to Strategic Resource Allocation in Acute Care Hospitals,
{\em European Journal of Operational Research} 140 (2002) 541-561.

\item Calvete. H.I., Gal\'{e}, C., Oliveros, M.J. and S\'{a}nchez-Valverde, B.: (Goal Programming)(E-Articles)
A Goal Programming Approach to Vehicle Routing Problems with Soft Time Windows,
{\em European Journal of Operational Research} 177 (2007) 1720-1733.

\item Chang, C.-T.: (Goal Programming)(E-Articles)
A Modified Goal Programming Model for Piecewise Linear Functions,
{\em European Journal of Operational Research} 139 (2002) 62-67.

\item Fan, Z.-P., Ma, J., Jiang, Y.-P., Sun, Y.-H. and Ma, L.: (Goal Programming)(E-Articles)
A Goal Programming Approach to Group Decision Making Based on Multiplicative Preference Relations and Fuzzy Preference Relations,
{\em European Journal of Operational Research} 174 (2006) 311-321.

\item Giokas, D. and Vassiloglou, M.: (Goal Programming)(E-Articles)
A Goal Programming Model for Bank Assets and Liabllitms Management,
{\em European Journal of Operational Research} 50 (1991) 48-60.

\item G\”{o}ken, H. and A\v{g}pak, K.: (Goal Programming)(E-Articles)
A Goal Programming Approach to Simple U-Line Balancing Problem,
{\em European Journal of Operational Research} 171 (2006) 577-585.

\item Hajidimitriou, Y.A. and Georgiou, A.C.: (Goal Programming)(E-Articles)
A Goal Programming Model for Partner Selection Decisions in International Joint Ventures,
{\em European Journal of Operational Research} 138 (2002) 649-662.

\item Hu, C.-F., Teng, C.-J. and Li, S.-Y.: (E-Articles)
A Fuzzy Goal Programming Approach to Multi-Objective Optimization Problem with Priorities,
{\em European Journal of Operational Research} 176 (2007) 1319-1333.

\item Kazemzadeh, R.B., Bashiri, M., Atkinson, A.C. and Noorossana, R.: (E-Articles)
A General Framework for Multiresponse Optimization Problems Based on Goal Programming,
{\em European Journal of Operational Research} 189 (2008) 421-429.

\item Khorramshahgol, R. and Okoruwa, A.A.: (Goal Programming)(E-Articles)
A Goal Programming Approach to Investment Decisions: A Case Study of Fund Allocation Among Different Shopping Malls,
{\em European Journal of Operational Research} 73 (1994) 17-22.

\item Kwak, N.K. and Schniederjans, M.J.: (Goal Programming)(E-Articles)
A Goal Programming Model for Improved Transportation Problem Solutions,
{\em Omega} 7 (1979) 367-370.

\item Lee, S.M. and Olson, D.L.: (Goal Programming)(E-Articles)
A Gradient Algorithm for Chance Constrained Nonlinear Goal Programming,
{\em European Journal of Operational Research} 22 (1985) 359-369.

\item Liu, F., Zhang, W.-G. and Wang, Z.-X: (Goal Programming)(E-Articles)
A Goal Programming Model for Incomplete Interval Multiplicative Preference Relations and Its Application in Group Decision-Making,
{\em European Journal of Operational Research} 218 (2012) 747-754.

\item Mirrazavi, S.K., Jones, D.F. and Tamiz, M.: (E-Articles)
A Comparison of Genetic and Conventional Methods for the Solution of the Goal Programmes,
{\em European Journal of Operational Research} 132 (2001) 594-602.

\item Pal, B.B. and Moitra, B.N.: (Goal Programming)(E-Articles)
A Goal Programming Procedure for Solving Problems with Multiple Fuzzy Goals Using Dynamic Programming,
{\em European Journal of Operational Research} 144 (2003) 480-491.

\item Romero, C.: (E-Articles)
A General Structure of Achievement Function for a Goal Programming Model,
{\em European Journal of Operational Research} 153 (2004) 675-686.

\item Samouilidis, J.E. and Pappas, I.A.: (Goal Programming)(E-Articles)
A Goal Programming Approach to Energy Forecasting,
{\em European Journal of Operational Research} 5 (1980) 321-331.

\item Wang, Y.-M. and Elhag, T.M.S.: (Goal Programming)(E-Articles)
A Goal Programming Method for Obtaining Interval Weights from an Interval Comparison Matrix,
{\em European Journal of Operational Research} 177 (2007) 458-471.

\item Wang, Z.-J. and Li, K.W.: (Goal Programming)(E-Articles)
A Multi-Step Goal Programming Approach for Group Decision Making with Incomplete Interval Additive Reciprocal Comparison Matrices,
{\em European Journal of Operational Research} 242 (2015) 890-900.

\item Yaghoobi, M.A. and Tamiz, M.: (Goal Programming)(E-Articles)
A Method for Solving Fuzzy Goal Programming Problems Based on Minmax Approach,
{\em European Journal of Operational Research} 177 (2007) 1580-1590.

\item Zanakis, S.H. and Gupta, S.K.: (E-Articles)
A Categorized Bibliographic Survey of Goal Programming,
{\em Omega} 13 (1985) 211-222.

\begin{equation}{\label{m}}\tag{M}\mbox{}\end{equation}

Continuous-Time Programming Problems.

\item Abrham, J. and Buie, R.N.:
Kuhn-Tucker Conditions and Duality in Continuous Programming,
{\em Utiltas Mathematica} 16 (1979) 15-37.

\item Buie, R.N. and Abrham, J.:
Some Remakrs Concerning Duality for Continuous-Time Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 114 (1986) 468-489.

\item Anderson, E.J., Nash, P. and Philpott, A.B. :
A Class of Continuous Network Flow Problems,
{\em Mathematics of Operations Research} 7 (1982) 501-514.

\item Anderson, E.J., Nash, P. and Perold, A.F. :
Some Properties of a Class of Continuous Linear Programs,
{\em SIAM J. Control and Optimization} 21 (1983) 758-765.

\item Anderson, E.J. and Philpott, A.B. :
Duality and Algorithm for a Class of Continuous Transportation Problems,
{\em Mathematics of Operations Research} 9 (1984) 222-231.

\item Anderson, E.J. and Philpott, A.B. :
A Continuous-Time Network Simplex Algorithm,
{\em Networks} 19 (1989) 395-425.

\item Anderson, E.J. and Philpott, A.B. :
On the Solutions of a Class of Continuous Linear Programs,
{\em SIAM Journal on Control and Optimization} 32 (1994) 1289-1296.

\item Anderson, E.J. and Pullan, M.C. :
Purification for Separated Continuous Linear Programs,
{\em Mathematical Methods of Operations Research} 43 (1996) 9-33.

\item Anderson, E.J. and Wu, S.-Y. :
The Continuous Complementarity Problem,
{\em Optimization} 22 (1991) 419-426.

\item Andreani, R., Goncalves, P.S. and Silva, G.N.:
Discrete Approximations for Strict Convex Continuous-Time Problems and
Duality,
{\em Computational and Applied Mathematics{ 23 (2004) 81-105.

\item Audet, C., Haddad, J. and Savard, G.:
Disjunctive Cuts for Continuous Linear Bilevel Programming,
{\em Optimization Letters} 1 (2007) 259-267.

\item Bauschke, H.H., Borwein, J.M. and Wang, X.:
Fitzpatrick Functions and Continuous Linear Monotone Operators,
{\em SIAM Journal on Optimization} 18 (2007) 789-809.

\item Brand\'{a}o, A.J.V., Rojas-Medar, M.A. and Silva, G.N.:
Nonsmooth Continuous-Time Optimization Problems: Necessary Conditions,
{\em Computers and Mathematics with Applications} 41 (2001) 1477-1486.

\item Buie, R.N. and Abrham, J.:
Numerical Solution to Continuous Linear Programming Problems,
{\em Zeitschrift f\”{u}r Operations Research} 17 (1993) 107-117.

\item de Oliveria, V.A. and Rojas-Medar, M.A.:
Continuous-Time Optimization Problems Involving Invex Functions,
{\em Journal of Mathematical Analysis and Applications} 327 (2007) 1320-1334.

\item Farr, W.H. and Hanson, M.A. :
Continuous Time Programming with Nonlinear Constraints,
{\em Journal of Mathematical Analysis and Applications} 45 (1974) 96-115.

\item Farr, W.H. and Hanson, M.A. :
Continuous Time Programming with Nonlinear Time-Delayed Constraints,
{\em Journal of Mathematical Analysis and Applications} 46 (1974) 41-61.

\item Fleischer, L. and Sethuraman, J.:
Efficient Algorithms for Separated Continuous Linear Programs:
The Multicommodity Flow Problem with Holding Costs and Extensions,
{\em Mathematics of Operations Research} 30 (2005) 916-938.

\item Grinold, R.C. :
Continuous Programming, Part One : Linear Objectives,
{\em Journal of Mathematical Analysis and Applications} 28 (1969) 32-51.

\item Grinold, R.C. :
Continuous Programming, Part Two : Nonlinear Objectives,
{\em Journal of Mathematical Analysis and Applications} 27 (1969) 639-655.

\item Grinold, R.C. :
Symmetric Duality for Continuous Linear Programs,
{\em SIAM J Appl. Math.} 18 (1970) 84-97.

\item Hanson, M.A. :
Duality for a Class of Infinite Programming Problems,
{\em SIAM Journal Applied Mathematics} 16 (1968) 318-323.

\item Hanson, M.A. and Mond, B. :
A Class of Continuous Convex Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 22 (1968) 427-437.

\item J\'{o}hannesson, B. and Hanson, M.A.:
On the Form of Solutions to the Linear Continuous Time Programming
Problems and a Conjecture by Tyndall,
{\em Journal of Mathematical Analysis and Applications} 111 (1985) 236-242.

\item Levinson, N. :
A Class of Continous Linear Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 16 (1966) 73-83.

\item Luo, X. and Bertsimas, D.: (Continuous Programming Problems)
A New Algorithm for State-Constrained Separated Continuous Linear Programs,
{\em SIAM Journal on Control and Optimization} 37 (1998) 177-210.

\item Marena, M. and Montrucchio, L.:
Neighborhood Turnpike Theorem for Continuous-Time Optimization Models,
{\em Journal of Optimization Theory and Applications} 101 (1999) 651-676.

\item Meidan, R. and Perold, A.F. :
Optimality Conditions and Strong Duality in Abstract and Continuous-Time Linear Programming,
{\em Journal of Optimization Theory and Applications} 40 (1983) 61-77.

\item Nobakhtian, S. and Pouryayevali, M.R.:
Optimality Criteria for Nonsmooth Continuous-Time Problems of
Multiobjective Optimization,
{\em Journal of Optimization Theory and Applications} 136 (2008) 69-76.

\item Nobakhtian, S. and Pouryayevali, M.R.:
Duality for Nonsmooth Continuous-Time Problems of Vector Optimization,
{\em Journal of Optimization Theory and Applications} 136 (2008) 77-85.

\item Papageorgiou, N.S. :
A Class of Infinite Dimensional Linear Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 87 (1982) 228-245.

\item Philpott, A.B. and Craddock, M.:
An Adaptive Discretization Algorithm for a Class of Continuous Network Programs,
{\em Networks} 26 (1995) 1-11.

\item Pullan, M.C.:
An Algorithm for a Class of Continuous Linear Programs,
{\em SIAM Journal on Control and Optimization} 31 (1993) 1558-1577.

\item Pullan, M.C.:
Forms of Optimal Solutions for Separated Continuous Linear Programs,
{\em SIAM Journal on Control and Optimization} 33 (1995) 1952-1977.

\item Pullan, M.C.:
A Duality Theory for Separated Continuous Linear Programs,
{\em SIAM Journal on Control and Optimization} 34 (1996) 931-965.

\item Pullan, M.C.:
Convergence of a General Class of Algorithms for Separated Continuous
Linear Programs,
{\em SIAM Journal on Optimization} 10 (2000) 722-731.

\item Pullan, M.C.:
An Extended Algorithm for Separated Continuous Linear Programs,
{\em Mathematical Programming} Ser. A 93 (2002) 415-451.

\item Reiland, T.W. :
Optimality Conditions and Duality in Continuous Programming I. Convex
Programs and a Theorem of the Alternative,
{\em Journal of Mathematical Analysis and Applications} 77 (1980) 297-325.

\item Reiland, T.W. :
Optimality Conditions and Duality in Continuous Programming II. The Linear
Problem Revisited,
{\em Journal of Mathematical Analysis and Applications} 77 (1980) 329-343.

\item Reiland, T.W. and Hanson, M.A. :
Generalized Kuhn-Tucker Conditions and Duality for Continuous Nonlinear
Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 74 (1980) 578-598.

\item Rojas-Medar, M.A., Brandao, J.V. and Silva, G.N.:
Nonsmooth Continuous-Time Optimization Problems: Sufficient Conditions,
{\em Journal of Mathematical Analysis and Applications} 227 (1998) 305-318.

\item Schechter, M. :
Duality in Continuous Linear Programming,
{\em Journal of Mathematical Analysis and Applications} 37 (1972) 130-141.

\item Scott, C.H. and Jefferson, T.R.:
Duality in Infinite-Dimensional Mathematical Programming: Convex Integral Functionals,
{\em Journal of Mathematical Analysis and Applications} 61 (1977) 251-261.

\item Singh, C. :
A Sufficient Optimality Criterion in Continuous Time Programming for
Generalized Convex Functions,
{\em Journal of Mathematical Analysis and Applications} 62 (1978) 506-511.

\item Singh, C. and Farr, W.H. :
Saddle-Point Optimality Criteria of Continuius Time Programming without
Differentiability,
{\em Journal of Mathematical Analysis and Applications} 59 (1977) 442-453.

\item Tyndall, W.F. :
An Extended Duality Theorem for Continuous Linera Programming Problems,
{\em SIAM J. Appl. Math.} 15 (1967) 1294-1298.

\item Tyndall, W.F. :
A Duality Theorem for a Class of Continuous Linera Programming Problems,
{\em SIAM J. Appl. Math.} 15 (1965) 644-666.

\item Weir, T., Hanson, M.A. and Mond, B.:
Generalized Concavity and Duality in Continuous Programming,
{\em Journal of Mathematical Analysis and Applications} 104 (1984) 212-218.

\item Weiss, G.:
A Simplex Based Algorithm to Solve Separated Continuous Linear Programs,
{\em Mathematical Programming}, Ser. A 115 (2008) 151=198.

\item Wirl, F.:
Pathways to Hopf Bifurcations in Dynamic Continuous-Time Optimization Problems,
{\em Journal of Optimization Theory and Applications} 91 (1996) 299-320.

\item Zalmai, G.J. :
Optimality Conditions and Lagrangian Duality in Continuous-Time Nonlinear
Programming,
{\em Journal of Mathematical Analysis and Applications} 109 (1985) 426-452.

\item Zalmai, G.J. :
A Continuous-Time Generalization of Gordan’s Tranposition Theorem,
{\em Journal of Mathematical Analysis and Applications} 110 (1985) 130-140.

\item Zalmai, G.J. :
The Frotz John and Kuhn-Tucker Optimality Conditions in
Continuous-Time Nonlinear Programming,
{\em Journal of Mathematical Analysis and Applications} 110 (1985) 503-518.

\item Zalmai, G.J. :
Sufficient Optimality Conditions in Continuous-Time Nonlinear Programming,
{\em Journal of Mathematical Analysis and Applications} 111 (1985) 130-147.

\item Zalmai, G.J. :
Duality in Continuous-Time Homogeneous Programming,
{\em Journal of Mathematical Analysis and Applications} 111 (1985) 433-448.

\item Zalmai, G.J. :
Duality for a Class of Continuous-Time Homogeneous Fractional Programming Problems,
{\em Zeitschrift f\”{u}r Operations Research} 30 (1986) 43-48.

\item Zalmai, G.J. :
Duality for a Class of Continuous-Time Fractional Programming Problems,
{\em Utilitas Mathematica} 31 (1987) 209-218.

\item Zalmai, G.J. :
Optimality Conditions and Duality for a Class of Continuous-Time
Programming Problems with Nonlinear Operator Equality and Inequality Constraints,
{\em Journal of Mathematical Analysis and Applications} 153 (1990) 309-330.

\item Zalmai, G.J. :
Optimality Conditions and Duality for a Class of Continuous-Time Generalized
Fractional Programming Problems,
{\em Journal of Mathematical Analysis and Applications} 153 (1990) 356-371.

\item Zalmai, G.J. :
Continuous-Time Generalized Fractional Programming,
{\em Optimization} 36 (1996) 195-217.

\item Zalmai, G.J. :
Continuous-Time Multiobjective Fractional Programming,
{\em Optimization} 37 (1996) 1-25.

\item Zalmai, G.J. :
Optimality Conditions and Duality Models for a Class of Nonsmooth
Continuous-Time Generalized Fractional Programming Problems,
{\em Optimization} 51 (2002) 353-399.

\item Zalmai, G.J. :
Proper Efficiency Conditions and Duality Models for a Class
of Nonsmooth Continuous-Time Multiobjective Fractional Programming Problems,
{\em Southeast Asian Bulletin of Mathematics} 27 (2003) 155-186.

\begin{equation}{\label{n}}\tag{N}\mbox{}\end{equation}

Inverse Optimization.

\item Ahmed, S. and Guan, Y.:
The Inverse Optimization Value Problem,
{\em Mathematical Programming}, Ser. A 102 (2005) 91-110.

\item Ahuja, R.K. and Orlin, J.B.: (Inverse Optimization)
Inverse Optimization,
{\em Operations Research} 49 (2001) 771-783.

\item Duin, C.W. and Volgenant, A.:
Some Inverse Optimization Problems under the Hamming Distance,
{\em European Journal of Operational Research} 170 (2006) 887-899.

\item Heuberger, C,:
Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results,
{\em Journal of Combinatorial Optimization} 8 (2004) 329-361.

\item Troutt, M.D., Tadisina, S.K., Sohn, C. and Brandyberry, A.A.:
Linear Programming System Identification,
{\em European Journal of Operational Research} 161 (2005) 663-672.

\item Yang, C. and Zhang, J.:
Two General Methods for Inverse Optimization Problems,
{\em Applied Mathematics Letters} 12 (1999) 69-72.

\item Zhang, J. and Liu, Z.:
Calculating Some Inverse Linear Programming Problems,
{\em Journal of Computational and Applied Mathematics} 72 (1996) 261-273.

\item Zhang, J. and Liu, Z.:
A Further Study on Inverse Linear Programming Problems,
{\em Journal of Computational and Applied Mathematics} 106 (1999) 345-359.

\begin{equation}{\label{o}}\tag{O}\mbox{}\end{equation}

Dynamic Programming.

\item Blackwell, D. :
Discrete Dynamic Programming.
{\em The Annals of Mathematical Statistics} 33 (1962) 719-726.

\item Blackwell, D :
Discounted Dynamic Programming.
{\em The Annals of Mathematical Statistics} 36 (1965) 226-235.

\item Chung, S.L., Hanson, F.B. and Xu, H.H. :
Parallel Stochastic Dynamic Programming : Finite Element Methods.
{\em Linear Algebra and Its Applications} 172 (1992) 197-218.

\item Hussien. M.L. and Abo-Sinna, M.A. :
Decomposition of Multiobjective Programming Problems by Hybrid Fuzzy-Dynamic
Programming.
{\em Fuzzy Sets and Systems} 60 (1993) 25-32.

\item Lai, H.-C. and Tanaka, K. :
On Continuous-time Discounted Stochasic Dynamic Programming.
{\em Applied Mathematics and Optimization} 23 (1991). 155-169.

\item Villarreal and Karwan, M.H. :
Multicriteria Dynamic Programming with an Application to the Integer Case.
{\em Journal of Optimization Theory and Applications} 38 (1982) 43-69.

\item White, D.J. :
Dynamic Programming and Probabilistic Costraints.
{\em Operations Research} 22 (1974) 654-664.

\item Yoshida, Y. :
Markov Chains with a Transition Possibility Measure and Fuzzy Dynamic
Programming.
{\em Fuzzy Sets and Systems} 66 (1994) 39-57.

\item Yu, P.L. and Leitmann, G. :
Nondominated Decisions and Cone Convexity in Dynamic Multicriteria Decision Problems.
{\em Journal of Optimization Theory and Applications} 14 (1976) 573-584.

 

\begin{equation}{\label{p}}\tag{P}\mbox{}\end{equation}

Minmax Regret Optimization.

\item Aissi, H., Bazgan, C. and Vanderpooten, D.:
Complexity of the Min-max and Min-max Regret Assignment Problems,
{\em Operations Research Letters} 33 (2005) 634-640.

\item Aissi, H., Bazgan, C. and Vanderpooten, D.:
Approximation of Min-max and Min-max Regret Versions of Some Combinatorial Optimization Problems,
{\em European Journal of Operational Research} 179 (2007) 281-290.

\item Aissi, H., Bazgan, C. and Vanderpooten, D.:
Min-Max and Min-Max Regret Version of Combinatorial Optimization Problems: A Survey,
{\em European Journal of Operational Research} 197 (2009) 427-438.

\item Averbakh, I.:
Minmax Regret Solutions for Minimax Optimization Problems with Uncertainty,
{\em Operations Research Letters} 27 (2000) 57-65.

\item Averbakh, I.: (Minmax Regret Optimization)
The Minmax Regret Permutation Flow-Shop Problem with Two Jobs,
{\em European Journal of Operational Research} 169 (2006) 761-766.

\item Averbakh, I.:
Minmax Regret Linear Resource Allocation Problems,
{\em Operations Research Letters} 32 (2004) 174-180.

\item Averbakh, I. and Lebedev:
Interval Data Minmax Regret Network Optimization Problems,
{\em Discrete Applied Mathematics} 138 (2004) 289-301.

\item Averbakh, I. and Lebedev:
On the Complexity of Minmax Regret Linear Programming,
{\em European Journal of Operational Research} 160 (2005) 227-231.

\item Conde, E.:
An Improved Algorithm for Selecting $p$ Times with Uncertain Returns According to the Minmax Regret Criterion,
{\em Mathematical Programming}, Ser. A, 100 (2004) 345-353.

\item Conde, E.:
Minmax Regret Location–Allocation Problem on a Network under Uncertainty,
{\em European Journal of Operational Research} 179 (2007) 1025-1039.

\item Conde, E.:
A Minmax Regret Approach to the Critical Path Method with Task Interval Times,
{\em European Journal of Operational Research} 197 (2009) 235-242.

\item Escoffier, B., Monnot, J. and Spanjaard, O.:
Some Tractable Instances of Interval Data Minmax Regret Problems,
{\em Operations Research Letters} 36 (2008) 424-429.

\item Kasperski, A. and Zieli\'{n}ski, P.:
An Approximation Algorithm for Interval Data Minmax Regret Combinatorial Optimization Problems,
{\em European Journal of Operational Research} 97 (2006) 177-180.

\item Kasperski, A. and Zieli\'{n}ski, P.:
On the Existence of an FPTAS for Minmax Regret Combinatorial Optimizations with Interval Data,
{\em Operations Research Letters} 35 (2007) 525-532.

\item Kasperski, A. and Zieli\'{n}ski, P.:
On the Approximation of Minmax (Regret) Network Optimization,
{\em Information Processing Letters} 109 (2009) 262-266.

\item Kasperski, A. and Zieli\'{n}ski, P.:
A 2-Approximation Algorithm for Interval Data Minmax Regret Sequencing Problems with the Total Flow Time Criterion,
{\em Operations Research Letters} 36 (2008) 343-344.

\item Lebedev, V. and Averbakh, I.:
Complexity of Minimizing the Total Flow Time with Interval Data and Minmax Regret Criterion,
{\em Discrete Applied Mathematics} 154 (2006) 2167-2177.

\item Yu, H.-I., Lin, T.-C. and Wang, B.-F.:
Improved Algorithms for the Minmax Regret 1-Center and 1-Median Problems,
{\em ACM Transactions on Algorithms} 4, No. 3 (2008) Article 36.

\begin{equation}{\label{q}}\tag{Q}\mbox{}\end{equation}

Multi-level Optimization.

\item Bard, J.F. and Falk, J.E.:
An Explicit Solution to the Multi-Level Programming Problem,
{\em Computers and Operations Research} 9 (1982) 77-100.

\item Bialas, W.F. and Karwan, M.H.:
Two-Level Linear Programming,
{\em Management Sciences} 30 (1984) 1004-1020.

\item Calvete, H.I. and Gal\'{e}, C.:
The Bilevel Linear/Linear Frcational Programming Problem,
{\em European Journal of Operational Research} 114 (1999) 188-197.

\item Calvete, H.I. and Gal\'{e}, C.:
On the Quasiconcave Bilevel Programming Problem,
{\em Journal of Optimization Theory and Applications} 98 (1998) 613-622.

\item Calvete, H.I. and Gal\'{e}, C.:
A Note on “Bilevel Linear Fractional Programming Problem”,
{\em European Journal of Operational Research} 152 (2004) 296-299.

\item Calvete, H.I., Gal\'{e}, C. and Maeto, P.M.:
A New Approach for Solving Linear Bilevel Problems Using
Genetic Algorithms,
{\em European Journal of Operational Research} 188 (2008) 14-28.

\item Candler, W. and Townsley, R.:
A Linear Two-Level Programming Problem,
{\em Computers and Operations Research} 9 (1982) 59-76.

\item Stein, O. and Still, G.:
On Generalized Semi-Infinite Optimization and Bilevel Optimization,
{\em European Journal of Operational Research} 142 (2002) 444-462.

\begin{equation}{\label{r}}\tag{R}\mbox{}\end{equation}

Second-Order Cone Programming.

\item Alizadeh, F. and Goldfarb, D.:
Second-Order Cone Programming,
{\em Mathematical Programming, Ser. B} 95 (2003) 3-51.

\item Bonnans, J.F. and Rami\'{r}ez C., H.:
Perturbation Analysis of Second-Order Cone Programming Problems,
{\em Mathematical Programming}, Ser. B., 104 (2005) 205-227.

\item Cai, Z. and Toh, K.-C.:
Solving Second Order Cone Programming via a Reduced Augmented System Approach,
{\em SIAM Journal on Optimization} 17 (2006) 711-737.

\item Chen, J.-S., Chen, X. and Tseng, P.:
Analysis of Nonsmooth Vector-Valued Functions Associated with Second-Order Cones,
{\em Mathematical Programming}, Ser. B, 101 (2004) 95-117.

\item Chi, X. and Liu, S.:
Sub-Quadratic Convergence of a Smoothing Newton Method for Second-Order Cone Programming,
{\em Journal of Applied Mathematics and Computation} 26 (2008) 489-502.

\item Chi, X. and Liu, S.:
A One-Step Smoothing Newton Method for Second-Order Cone Programming,
{\em Journal of Computational and Applied Mathematics} 223 (2009) 114-123.

\item Erdo\v{g}an, E. and Iyengar, G.:
An Active Set Method for Single-Cone Second-Order Cone Programs,
{\em SIAM Journal on Optimization} 17 (2006) 459-484.

\item Goldfarb, D. and Scheinberg, K.:
Product-Form Cholesky Factorization in Interior Point Methods for Second-Order Cone Programming,
{\em Mathematical Programming}, Ser. A, 103 (2005) 153-179.

\item Kato, H. and Fukushima, M.:
An SQP-type Algorithm for Nonlinear Second-Order Cone Programs,
{\em Optimization Letters} 1 (2007) 129-144.

\item Kuo, Y.-J. and Mittelmann, H.D.:
Interior Point Methods for Second-Order Cone Programming and OR Applications,
{\em Computational Optimization and Applications} 28 (2004) 255-285.

\item Liu, Y.-J. and Zhang, L.-W.:
Convergence Analysis of the Augmented Lagrangian Method for Nonlinear Second-Order Cone Optimization Problems,
{\em Nonlinear Analysis} 67 (2007) 1359-1373.

\item Lobo, M.S., Vandenberghe, L., Boyd, S. and Lebret, H.:
Applications of Second-Order Cone Programming,
{\em Linear Algebra and Its Applications} 284 (1998) 193-228.

\item Pan, S.H. and Chen, J.-S.:
Proximal-Like Algorithm Using the Quasi D-Function for Convex Second-Order Cone Programming,
{\em Journal of Optimization Theory and Applications} 138 (2008) 95-113.

\item Pan, S.H. and Chen, J.-S.:
A Class of Interior Proximal-Like Algorithms for Convex Second-Order Cone Programming,
{\em SIAM Journal on Optimization} 19 (2008) 883-910.

\item Sim, C.-K. and Zhao, G.:
A Note on Treating a Second Order Cone Program as a Special Case of a Semidefinite Program,
{\em Mathematical Programming}, Ser. A, 102 (2005) 609-613.

\item Xia, Y.:
A Newton’s Method for Perturbed Second-Order Cone Programs,
{\em Computational Optimization and Applications} 37 (2007) 371-408.

\item Xia, Y. and Alizadeh, F.:
The $Q$ Method for Second Order Cone Programming,
{\em Computers and Operations Research} 35 (2008) 1510-1538.

\begin{equation}{\label{s}}\tag{S}\mbox{}\end{equation}

Semi-Infinite Programming.

\item Amaya, J. and Goberna, M.A.:
On the Stability of Linear Systems with an Exact Constraint Set,
{\em Mathematical Methods of Operations Research} 63 (2006) 107-121.

\item Betr\'{o}, B.:
An Accelerated Central Cutting Plane Algorithm for Linear Semi-Infinite Programming,
{\em Mathematical Programming} 101 (2004) 479-495.

\item Borwein, J.M.:
The Limiting Lagrangian as a Consequence of Helley’s Theorem,
{\em Journal of Optimization Theory and Applications} 33 (1981) 497-513.

\item C\'{a}novas, M.J., Dontchev, A.L., L\'{o}pez, M.A. and Parra, J.:
Metric Regularity of Semi-Infinite Constraint Systems,
{\em Mathematical Programming} Ser. B. 104 (2005) 329-346.

\item C\'{a}novas, M.J., G\'{o}mez-Senent, F.J. and Parra, J.:
On the Lipschitz Modulus of the Argmin Mapping in Linear Semi-Infinite Optimization,
{\em Set-Valued Analysis} 16 (2008) 511-538.

\item C\'{a}novas, M.J., Hantoute, A., L\'{o}pez, M.A. and Parra, J.:
Stability of Indices in the KKT Conditions and Metric Regularity in Convex Semi-Infinite Optimization,
{\em Journal of Optimization Theory and Applications} 139 (2008) 485-500.

\item C\'{a}novas, M.J., Klatte, D. L\'{o}pez, M.A. and Parra, J.:
Metric Regularity in Convex Semi-Infinite Optimization under Canonical Perturbations,
{\em SIAM Journal on Optimization} 18 (2007) 717-732.

\item C\'{a}novas, M.J., L\'{o}pez, M.A. and Parra, J.:
Stability of Linear Inequality Systems in a Parametric Setting,
{\em Journal of Optimization Theory and Applications} 125 (2005) 275-297.

\item C\'{a}novas, M.J., L\'{o}pez, M.A., Parra, J. and Todorov, M.I.:
Stability and Well-Posedness in Linear Semi-Infinite Programming,
{\em SIAM Journal on Optimization} 10 (1999) 82-98.

\item C\'{a}novas, M.J., L\'{o}pez, M.A., Parra, J. and Todorov, M.I.:
Solving Strategies and Well-Posedness in Linear Semi-Infinite Programming,
{\em Annals of Operations Research} 101 (2001) 171-190.

\item C\'{a}novas, M.J., L\'{o}pez, M.A., Parra, J. and Toledo, F.J.:
Distance to Ill-Posedness and the Consistency Value of Linear Semi-Infinite Inequality Systems,
{\em Mathematical Programming}, Ser. A, 103 (2005) 95-126.

\item C\'{a}novas, M.J., L\'{o}pez, M.A., Parra, J. and Toledo, F.J.:
Distance to Solvability/Unsolvability in Linear Optimization,
{\em SIAM Journal on Optimization} 16 (2006) 629-649.

\item C\'{a}novas, M.J., L\'{o}pez, M.A., Parra, J. and Toledo, F.J.:
Lipschitz Continuity of the Optimal Value via Bounds on the Optimal Set in Linear Semi-Infinite Optimization,
{\em Mathematics of Operations Research} 31 (2006) 478-489.

\item C\'{a}novas, M.J., L\'{o}pez, M.A., Parra, J. and Toledo, F.J.:
Sufficient Conditions for Total Ill-Posedness in Linear Semi-Infinite Optimization,
{\em European Journal of Operational Research} 181 (2007) 1126-1136.

\item Charnes, A., Cooper, W.W. and Kortanek, K. :
Duality in Semi-Infinite Programs and Some Works of Haar and Carath\'{e}odory,
{\em Management Science} 9 (1963) 209-228.

\item Charnes, A., Cooper, W.W. and Kortanek, K. :
On Representations of Semi-Infinite Programs which have no Duality Gap,
{\em Management Science} 12 (1965) 113-121.

\item Colgen, R.:
Necessary Conditions for Upper Semicontinuity in Parametric Semi-Infinite Programming,
{\em Journal of Optimization Theory and Applications} 48 (1986) 65-79.

\item Fajardo, M.D. and Lopez, M.A.:
Locally Farkas-Minkowski Systems in Convex Semi-Infinite Programming,
{\em Journal of Optimization Theory and Applications} 103 (1999) 313-335.

\item Fang, S.-C., Lin, C.-J. and Wu, S.-Y.:
Solving Quadratic Semi-Infinite Programming Problems by Using Relaxed Cutting-Plane Scheme,
{\em Journal of Computational and Applied Mathematics} 129 (2001) 89-104.

\item Fang, S.-C. and Wu, S.-Y.:
Solving Min-Max Problems and Linear Semi-Infinite Programs,
{\em Computers and Mathematics with Applications} 32, \#6 (1996) 87-93.

\item Fang, S.-C., Wu, S.-Y. and Sun, J.:
An Analytic Center Cutting Plane Method for Solving Semi-Infinite Variational Inequality Problems,
{\em Journal of Global Optimization} 28 (2004) 141-152.

\item Fischer, T.:
Strong Unicity and Alternation for Linear Optimization,
{\em Journal of Optimization Theory and Applications} 69 (1991) 251-267.

\item Gaya, V.E., L\'{o}pez, M.A. and De Serio, V.N.V.:
Stability in Convex Semi-Infinite Programming and Rates of Convergence of Optimal Solutions of Discretized Finite Subproblems,
{\em Optimization} 52 (2003) 693-713.

\item Goberna, M.A., G\'{o}mez, S., Guerra, F. and Todorov, M.I.:
Sensitivity Analysis in Linear Semi-Infinite Programming: Perturbing Cost and Right-Hand-Side Coefficients,
{\em European Journal of Operational Research} 181 (2007) 1069-1085.

\item Goberna, M.A., Jornet, V., Puente, R. and Todorov, M.I.: (Semi-Infinite Programming)
Analytical Linear Inequality Systems and Optimization,
{\em Journal of Optimization Theory and Applications} 103 (1999) 95-119.

\item Goberna, M.A. and L\'{o}pez, M.A.:
Conditions for the Uniqueness of the Optimal Solution in Linear Semi-Infinite Programming,
{\em Journal of Optimization Theory and Applications} 72 (1992) 225-246.

\item Goberna, M.A. and L\'{o}pez, M.A.:
Optimal Value Function in Semi-Infinite Programming,
{\em Journal of Optimization Theory and Applications} 59 (1988) 261-279.

\item Goberna, M.A. and L\'{o}pez, M.A. :
Topological Stability of Linear Semi-Infinite Inequality Systems,
{\em Journal of Optimization Theory and Applications} 89 (1996) 227-236.

\item Goberna, M.A. and L\'{o}pez, M.A.:
Linear Semi-Infinite Programming Theory: An Updated Survey,
{\em European Journal of Operational Research} 143 (2002) 390-405.

\item Goberna, M.A., L\'{o}pez, M.A. and Todorov, M.I.:
Unicity in Linear Optimization,
{\em Journal of Optimization Theory and Applications} 86 (1995) 37-56.

\item Goberna, M.A., L\'{o}pez, M.A. and Todorov, M.I.:
Stability Theory for Linear Inequality Systems,
{\em SIAM Journal on Matrix Analysis and Applications} 17 (1996) 730-743.

\item Goberna, M.A., L\'{o}pez, M.A. and Todorov, M.I.:
A Generic Results in Linear Semi-Infinite Optimization,
{\em Applied Mathematics and Optimization} 48 (2003) 181-193.

\item Goberna, M.A. and Todorov, M.I.:
Generic Primal-Dual Solvability in Continuous Linear Semi-Infinite Programming,
{\em Optimization} 57 (2008) 239-248.

\item G\'{o}mez, J.A., Bosch, P.J. and Amaya, J.:
Duality for Inexact Semi-Infinite Linear Programming,
{\em Optimization} 54 (2005) 1-25.

\item Gugat, M.: (Semi-Infinite Programming)
Convex Semi-Infinite Parametric Programming: Uniform Convergence of the Optimal Value Functions of Discretized Problems,
{\em Journal of Optimization Theory and Applications} 101 (1999) 191-201.

\item Helbig, S. and Todorov, M.I.:
Unicity Results for General Linear Semi-Infinite Optimization Problem Using a New Concept of Active Constraints,
{\em Applied Mathematics and Optimization} 38 (1998) 21-43.

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Semi-Infinite Programming: Theory, Methods and Applications,
{\em SIAM Review} 35 (1993) 380-429.

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An Approximation Approach to Non-Strictly Convex Quadratic Semi-Infinite Programming,
{\em Journal of Global Optimization} 30 (2004) 195-206.

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Semi-Infinite Optimization: Structure and Stability of the Feasible Set,
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Nonsmooth Semi-infinite Programming Problems with Mixed Constraints,
{\em Journal of Mathematical Analysis and Applications} 351 (2009) 170-181.

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Path-Following Proximal Approach for Solving Ill-Posed Convex Semi-Infinite Programming Problems,
{\em Journal of Optimization Theory and Applications} 90 (1996) 113-137.

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A Pathological Semi-Infinite Program Verifying Karlovitz’s Conjecture,
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Semi-Infinite Trasportation Problems,
{\em J. Math. Anal. Appl.} 88 (1982) 555-565.

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An Algorithm Constructing Solutions for a Family of Linear Semi-Infinite Problems,
{\em Journal of Optimization Theory and Applications} 110 (2001) 585-609.

\item Kryazhimskii, A.V. and Ruszczy\'{n}ski, A.:
Constraint Aggregation in Infinite-Dimensional Spaces and Applications,
{\em Mathematics of Operations Research} 26 (2001) 769-795.

\item Le\'{o}n, T. and Vercher, E.:
New Descent Rules for Solving the Linear Semi-Infinite Programming Problem,
{\em Operations Research Letters} 15 (1994) 105-114.

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Solving a Class of Fuzzy Linear Programs by Using Semi-Infinite Programming Techniques,
{\em Fuzzy Sets and Systems} 146 (2004) 235-252.

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A Smoothing Newton Method for Semi-Infinite Programming,
{\em Journal of Global Optimization} 30 (2004) 169-194.

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Parametric Linear Semi-Infinite Programming,
{\em Applied Mathematics Letters} 9, \#3 (1996) 89-96.

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An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming,
{\em SIAM J. on Optimization} 8 (1998) 443-456.

\item Lin, C.-J., E.K. Yang, Fang, S.-C. and Wu, S.-Y.:
Implementation of an Inexact Approach to Solving Linear Semi-Infinite Programming Problems,
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Existence Results for Primal and Dual Generalized Vector Equilibrium Problems with Applications to Generalized Semi-Infinite Programming,
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Existence Theorems for Bilevel Problem with Applications to Mathematical Program with Equilibrium Constraint and Semi-Infinite Problem,
{\em Journal of Optimization Theory and Applications} 137 (2008) 27-40.

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Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming,
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Higher-Order Necessary Conditions for Infinite and Semi-Infinite Optimization,
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Semi-Infinite Programming,
{\em European Journal of Operational Research} 180 (2007) 491-518.

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Convex Semi-Infinite Games,
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An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems,
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Semismooth Newton Methods for Solving Semi-Infinite Programming Problems,
{\em Journal of Global Optimization} 27 (2003) 215-232.

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Discretization Methods for the Solution of Semi-Infinite Programming Problems,
{\em Journal of Optimization Theory and Applications} 71 (1991) 85-103.

\item R\”{u}ckmann, J.-J.:
On Existence and Uniqueness of Stationary Points in Semi-Infinite Optimization,
{\em Mathematical Programming}, Ser. A 86 (1999) 387-415.

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First-Order Optimality Conditions in Generalized Semi-Infinite Programming,
{\em Journal of Optimization Theory and Applications} 101 (1999) 677-691.

\item R\”{u}ckmann, J.-J. and Shapiro, A.:
Second-Order Optimality Conditions in Generalized Semi-Infinite Programming,
{\em Set-Valued Analysis} 9 (2001) 169-186.

\item Shapiro, A.:
On Duality Theory of Convex Semi-Infinite Programming,
{\em Optimization} 54 (2005) 535-543.

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A Primal-Dual Infeasible-Interior-Point Algorithm for Linear Semi-Infinite
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Combined Entropic Regularization and Path-Following Method for Solving Finite Convex Min-Max Problems Subject to Infinitely Many Linear Constraints,
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Infinite (Semi-Infinite) Problems to Characterize the Optimality of Nonlinear Optimization Problems,
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On Optimality Conditions for Generalized Semi-Infinite Programming Problems,
{\em Journal of Optimization Theory and Applications} 104 (2000) 443-458.

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A Globally Convergent SQP Method for Semi-Infinite Nonlinear Optimization,
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One-Parametric Semi-Infinite Optimization: On the Stability of the Feasible Set,
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Kuratowski COnvergence of the Efficient Sets in the Parametric Linear Vector Semi-Infinite Optimization,
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Extensions of the Kuhn-Tucker Constraint Qualification to Generalized Semi-Infinite Programming,
{\em SIAM J. Optimization} 15 (2005) 926-937.

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A Perturbation Method for Solving Linear Semi-Infinite Programming Problems,
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Solving Convex Programs with Infinitely Many Linear Constraints by a
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{\em Computers and Mathematics with Applications} 38 (1999) 23-33.

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Relaxed Cutting Plane Method for Solving Semi-Infinite Programming Problems,
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First Order Optimality Conditions for Generalized Semi-infinite Programming Problems,
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Conditioning of Semidefinite Programs,
{\em Mathematical Programming} 85 (1999) 525-540.

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Linear Programming, Complexity Theory and Elementary Functional Analysis,
{\em Mathematical Programming} 70 (1995) 279-351.

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The Rate of Convergence of the Augmented Lagrangian Method for Nonlinear Semidefinite Programming,
{\em Mathematical Programming}, Ser. A, 114 (2008) 349-391.

\begin{equation}{\label{t}}\tag{T}\mbox{}\end{equation}

Set Optimization.

\item Alonso, M. and Rodriguez-Marin, L.: (E-article and paper article)
Optimality Conditions for Set-Valued Maps with Set Optimization,
{\em Nonlinear Analysis} 70 (2009) 3057-3064.

\item Araya, Y.: (E-Article)
Four types of nonlinear scalarizations and some applications in set optimization,
{\em Nonlinear Analysis} 75 (2012) 3821-3835.

\item Crespia, G.P., Hamel, A.H. and Schragea, C: (E-Article)
A Minty variational principle for set optimization,
{\em Journal of Mathematical Analysis and Applications} 423 (2015) 770-796.

\item Dempe, S. and Gadhi, N.: (E-Article)
Necessary optimality conditions for bilevel set optimization problems,
{\em Journal of Global Optimization} 39 (2007) 529-542.

\item Dempe, S. and Gadhi, N.: (E-Article)
Second order optimality conditions for bilevel set optimization problems,
{\em Journal of Global Optimization} 47 (2010) 233-245.

\item Guti\'{e}rrez, C., Jim\'{e}nez, B., Miglierina, E. and Molho, E.: (E-Article)
Scalarization in Set Optimization With Solid and Nonsolid Ordering Cones,
{\em Journal of Global Optimization}

\item Guti\'{e}rrez, C., Miglierina, E., Molhoc, E. and Novod V.:(E-Article)
Pointwise well-posedness in set optimization with cone proper sets,
{\em Nonlinear Analysis} 75 (2012) 1822-1833.

\item Hamel, A.H. and L\”{o}hne, A: (E-Article)
Lagrange Duality in Set Optimization,
{\em Journal of Optimization Theory and Applications} 161 (2014) 368-397

\item Jahn, J.: (E-Article)
Vectorization in Set Optimization
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New Order Relations in Set Optimization,
{\em Journal of Optimization Theory and Applications} 148 (2011) 209-236.

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Convexity for Set-Valued Maps,
{\em Applied Mathematics Letters} 9 (1996) 97-101.

\item Kuroiwa, D.: (E-Article)
On Set-Valued Optimization,
{\em Nonlinear Analysis} 47 (2001) 1395-1400.

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On Cone Convexity of Set-Valued Maps,
{\em Nonlinear Analysis} 30 (1997) 1487-1496.

\item Long, X.J. and Peng, J.W.: (E-Article)
Generalized B-Well-Posedness for Set Optimization Problems
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\item Xu, Y.D. and Li, S.J.: (E-Article)
Continuity of the solution set mappings to a parametric set optimization problem,
{\em Optimization Letters} 8 (2014) 2315-2327.

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Well-posedness for set optimization problems,
{\em Nonlinear Analysis} 71 (2009) 3769-3778.

\begin{equation}{\label{u}}\tag{U}\mbox{}\end{equation}

Stochastic Optimization.

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Chance-Constrained Programming,
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Chance Constrainted Programs with Normal Deviates and Linear Decision Rules,
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Chance Constraints and Normal Deviates,
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{\em Management Science} 12 (1965) 83-112.

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Some Special P-Models in Chance-Constrained Programming,
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Linear Programming under Uncertainty.
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Large-Scale Stochastic Linear Programs – Importance Sampling and Benders
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{\em Stochastics} 25 (1988) 15-42.

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{\em Mathematical Programming} Ser. A 89 (2000) 55-77.

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\item Dentcheva, D. and Ruszcy\'{n}ski, A.:
Optimization with Stochastic Dominance Constraints,
{\em SIAM Journal on Optimization} 14 (2003) 548-566.

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Optimality and Duality Theory for Stochastic Optimization Problems
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{\em Mathematical Programming} Ser. A 99 (2004) 329-350.

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Dual Methods for Probabilistic Optimization Problems,
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Convexification of Stochastic Ordering,

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Semi-Infinite Probablistic Optimization: First-Order Stochastic Dominance
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{\em Optimization} 53 (2004) 583-601.

\item Dentcheva, D. and Ruszcy\'{n}ski, A.:
Inverse Stochastic Dominance Constraints and Rank Dependent Expected Utility
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A Heuristic Algorithm for a Chance Constrained Stochastic Program,
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Second-Order Lower Bounds on the Expectation of a Convex Function,
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An Algorithm for the Minimum-Risk Problem of Stochastic Programming.
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Bounding the Expectation of a Saddle Function with Application to
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Duality for Stochastic Programming Interpreted as LP in $L_{p}$ Space.
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Bounding the Probability of Success of Stochastic Methods for Global
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Lagrange Multipliers in Stochastic Programming.
{\em SIAM Journal of Control and Optimization} 30 (1992) 1-10.

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Solving SLP Recourse Problems with Arbitrary Multivariate Distributions –
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Multistage Stochastic Programming : Error Analysis for the Convex Case,
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Computation in Discrete Stochastic Programs with Recourse.
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Computation in Discrete Stochastic Programs with Recourse,
{\em Operations Research} 21 (1973) 112-122.

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Recursive Stochastic Algorithms for Global Optimization in ${\bf R}^{d}$,
{\em SIAM J. Control and Optimization} 29 (1991) 999-1018.

\item Gondzio, J. \& Ruszczy\'{n}ski, A. :
Sensitivity Method for Basis Inverse Representation in Multistage Stochastic
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Estimated Stochastic Programs with Chance Constraints,
{\em European Journal of Operational Research} 101 (1997) 285-305.

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Stability of Multistage Stochastic Programs,
{\em SIAM Journal on Optimization} 17 (2006) 511-525.

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Risk Criteria in a Stochastic Knapsack Problem,
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Monte Carlo Simulation and Global Optimization without Parameters,
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Stochastic Decomposition : An Algotithm for Two-stage Linear Programs
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Finite Master Programs in Regularized Stochastic Decomposition,
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Stochastic Decomposition : An Algorithm for Two-Stage Linear Programs with
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{\em Mathematics of Operations Research} 16 (1991) 650-669.

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Duality and Statistical Tests of Optimality for Two Stage
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Statistical Approximations for Stochastic Linear Programming Problems,
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Chance-Constrained Programming with 0-1 or Bounded Continuous Decison Variables.
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Cross Decomposition Applied to the Stochastic Transportation Problem,
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Stochastic Linear Knapsack Problem : Probability Maximization Model,
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Chance-Constrained Programming with Joint Constraints.
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Parallel Factorization of Strucutred Matrices Arising in Stochastic Programming,
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A Stochastic Programming Model.
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Epi-consistency of Convex Stochastic Programs.
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Asymptotic Theory for Solutions in Statistical Estimation and Stochastic
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{\em Mathematics of Operation Research} 18 (1993) 148-162.

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Constraint Aggregation in Infinite-Dimensional Spaces and Applications,
{\em Mathematics of Operations Research} 26 (2001) 769-795.

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Neceaasry Conditions for Continuous Parameter Scochastic Optimization Problems,
{\em SIAM J. Control} 10 (1972) 550-565.

\item Laporte, G. \& Louveaux, F.V. :
Then Integer L-Shaped Method for Stochastic Integer Programs with Complete
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Stochastic Programming : An Interactive Multicriteria Approach.
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Approximations to Stochastic Programs with Complete Recourse.
{\em SIAM Journal of Control and Optimization} 28 (1990) 382-394.

\item Li, X. and Wang, J. :
Approximate Feasible Direction Method for Stochastic Programming Problems
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Stochastic Programming with Simple Integer Recourse,
{\em Mathematical Programming} 61 (1993) 301-325.

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A Heuristic Procedure for Stochastic Integer Programs with Complete
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{\em European Journal of Operational Research} 171 (2006) 879-890.

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Monte Carlo Bounding Techniques for Determining Solution Quality in
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Dual Variables in Two-Stage Linear Programming under Uncertainty,
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Relaxation of Linear Programming Problems with First Order Stochastic
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Valid Inequalities and Restrictions for Stochastic Programming Problems
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Multistage Stochastic Programming with Recourse : The Equivalent
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When is Multistage Stochastic Programming Problem Well-defined ?
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Multistage Stochastic Programming with Rescourse as Mathematical
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\item Piccioni, M. :
A Combined Multistart-Annealing Algorithms for Continuous Global Optimization,
{\em Computers Math. Applic.} 21 (1991) 173-179.

\item Powell, W., Ruszcy\'{n}ski, A. and Topaloglu, H.:
Learning Algorithms for Separable Approximations of Discrete Stochastic
Optimization Problems,
{\em Mathematics of Operations Research} 29 (2004) 814-836.

\item Rockafellar, R.T. and Wets, R.J.-B. :
Scenarios and Policy Aggregation in Optimization under Uncertainty.
{\em Mathematics of Operations Research} 16 (1991) 119-147.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Continuous versus Measurable Recourse in N-Stage Stochastic Programming,
{\em J. Math. Anal. Appl.} 48 (1974) 836-859.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Stochastic Convex Programming : Kuhn-Tucker Conditions,
{\em J. Mathematical Economics} 2 (1975) 349-370.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Nonanticipativity and ${\cal L}^{1}$-Martihgales in Stochastic Optimization
Problems,
{\em Mathematical Programming Study} 6 (1976) 170-187.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Stochastic Convex Programming : Basic Duality,
{\em Pacific J. Math.} 62 (1976) 173-195.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Stochastic Convex Programming : Singular Multipliers and Extended Duality,
{\em Pacific J. Math.} 62 (1976) 507-522.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Stochastic Convex Programming : Relatively Complete Recourse and Induced
Feasibility,
{\em SIAM J. Control and Optimization} 14 (1976) 574-589.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Measures as Lagrange Multipliers in Multistage Stochastic Programming,
{\em J. Math. Anal. Appl.} 60 (1977) 301-313.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
The Optimal Recourse Problem in Discrete Time : ${\cal L}^{1}$-Multipliers for Inequality Constraints,
{\em SIAM J. Control and Optimization} 16 (1978) 16-36.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
On the Interchange of Subdifferentiation and Conditional Expectation for Convex Funtionals,
{\em Stochastics} 7 (1982) 173-182.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Generalized Linear-Quadratic Problems of Deterministic and Stochastic
Optimal Control in Discrete Time,
{\em SIAM J. Control and Optimization} 28 (1990) 810-822.

\item Rockafellar, R.T. \& Wets, R.J.-B. :
Scenarios and Policy Aggregation in Optimization under Uncertainty,
{\em Mathematics of Operation Research} 16 (1991) 119-147.

\item Romisch, W. and Schultz, R. :
Distribution Sensitivity in Stochastic Programming.
{\em Mathematical Programming} 50 (1991) 197-226.

\item R\”{o}misch, W. \& Schultz, R. :
Stability of Solutions for Stochastic Programs with Complete Recourse,
{\em Mathematics of Operation Research} 18 (1993) 590-609.

\item Ruszcy\'{n}ski, A. :
Parallel Decomposition of Multistage Stochastic Programming Problems,
{\em Mathematical Programming} 58 (1993) 201-228.

\item Ruszcy\'{n}ski, A. and Shapiro, A.:
Optimization of Convex Risk Functions,
{\em Mathematics of Operations Research} 31 (2006) 433-452.

\item Ruszcy\'{n}ski, A. and Shapiro, A.:
Conditional Risk Mappings,
{\em Mathematics of Operations Research} 31 (2006) 544-561.

\item Ruszcy\'{n}ski, A. and \'{S}wietanowski, A.:
Accelerating the Regularized Decomposition Method for Two Stage Stochastic
Linear Problems,
{\em European Journal of Operational Research} 101 (1997) 328-342.

\item Ruszcy\'{n}ski, A. and Vanderbei, R.J.:
Frontiers of Stochastically Nondominated Portfolios,
{\em Econometrica} 71 (2003) 1287-1297.

\item Schultz, R. :
Continuity Properties of Expectation Functions in Stochastic Integer
Programming,
{\em Mathematics of Operation Research} 18 (1993) 578-589.

\item Sen, S. :
Subgradient Decomposiiton and Differentiability of the Recourse Function
of a Two Stage Stochastic Linear Program
{\em Operations Research Letters} 13 (1993) 143-148.

\item Shapiro, A. :
Asymptotic Properties of Statistical Estimators in Stochastic Programming,
{\em The Annals of Statitics} 17 (1989) 841-858.

\item Shapiro, A.: (Stochastic Programming)
Asymptotic Analysis of Stochastic Programs,
{\em Annals of Operations Research} 30 (1991) 169-186.

\item Shapiro, A. :
Asymptotic Behavior of Optimal Solutions in Stochastic Programming,
{\em Mathematics of Operation Research} 18 (1993) 829-845.

\item Shapiro, A.:
Inference of Statistical Bounds for Multistage Stochastic Programming
Problems,
{\em Mathematical Methods of Operations Research} 58 (2003) 57-68.

\item Shapiro, A.:
On Complexity of Multistage Stochastic Programs,
{\em Operations Research Letters} 34 (2006) 1-8.

\item Shapiro, A.:
Stochastic Programming with Equilibrium Constraints,
{\em Journal of Optimization Theory and Applications} 128 (2006) 223-243.

\item Shapiro, A.:
Stochastic Programming Approach to Optimization under Uncertainty,
{\em Mathematical Programming} Ser. B, 112 (2008) 183-220.

\item Shapiro, A. and Ahmed, S.:
On a Class of Minimax Stochastic Programs,
{\em SIAM Journal on Optimization} 14 (2004) 1237-1249.

\item Shapiro, A. and Homem-de-Mello:
A Simulation-Based Approach to Two-Stage Stochastic Programming with
Recourse,
{\em Mathematical Programming} 81 (1998) 301-325.

\item Shapiro, A., Homem-de-Mello, T. and Kim, J.:
Conditioning of Convex Piecewise Linear Stochastic Programs,
{\em Mathematical Programming} Ser. A 94 (2002) 1-19.

\item Shonkwiler, R. \& Vleck, E.V. :
Parallel Speed-Up of Monte Carlo Methods for Global Optimization,
{\em J. Complexity} 10 (1994) 64-95.

\item Sengupta, J.K. :
Non-parametric Approach to Stochastic Linear Programming.
{\em International Journal of Systems Sciences} 24 (1993) 857-871.

\item Sengupta, J.K., Tintner, G. \& Morrison, B. :
Stochastic Linear Programming with Applications to Economic Models,
{\em Economica} 30 (1963) 262-276.

\item Slyke, R.M.V. and Wets, R. :
Programming under Uncertainty and Stochastic Optimal Control.
{\em J. SIAM Control} 4 (1966) 179-193.

\item Slyke, R.M.V. and Wets, R. :
L-Shaped Liner Programs with Applications to Optimal Control and Stochastic
Programming.
{\em SIAM Journal of Applied Mathematics} 17 (1969) 638-663.

\item Sniedovich, M. :
Preference Order Stochastic Knapsack Problems : Methodological Issues,
{\em J. Operational Research Society} 31 (1980) 1025-1032.

\item Steinberg, E. \& Parks, M.S. :
A Preference Order Dynamic Program for a Knapsack Problem with Stochastic
Rewards,
{\em J. Operational Research Society} 30 (1979) 141-147.

\item Stolc, L. :
Stochastic Linear Programming Method for Right-Hand Sides Random Vector.
{\em International Journal of Systems Sciences} 22 (1991) 1197-1208.

\item Swierniak, A.P. :
On Optimality in an Uncertain Environment,
{\em J. Optimization Theory and Applications} 71 (1991) 189-193.

\item Symond, G.H. :
Chance-Constrained Equivalents of Some Stochastic Programming Problems,
{\em Operations Research} 16 (1968) 1152-1159.

\item Teghem, J., Dufrane, D. \& Thauvoye, M. :
STRANGE : An Interative Method for Multi-objective Linear Programming under
Unceratinty,
{\em European J. Operational Research} 26 (1986) 65-82.

\item Tintner, G. :
A Note on Stochastic Linear programming,
{\em Econometrica} 28 (1960) 490-495.

\item Todd, M.J. :
Probabilistic Models for Linear Programming,
{\em Mathematics of Operations Research} 16 (1991) 671-693.

\ite, Urli, B. and Nadeau, R.:
PROMISE/Scenarios: An Interactive Method for Multiobjective Stochastic
Linear Programming under Partial Uncertainty,
{\em European Journal of Operational Research} 155 (2004) 361-372.

\item Walkup, D.W. and Wets, R.J.-B. :
Stochastic Programs with Recourse.
{\em SIAM J. Appl. Math.} 15 (1967) 1299-1315.

\item Walkup, D.W. \& Wets, R. J.-B. :
A Note on Decision Rules for Stochastic Programs,
{\em J. Computer and System Sciences} 2 (1968) 305-311.

\item Walkup, D.W. and Wets, R.J.-B. :
Stochastic Programs with Recourse II : On the Continuity of the Objective.
{\em SIAM J. Appl. Math.} 17 (1969) 98-103.

\item Wallace, S.W. :
Solving Stochastic Programs with Network Recourse,
{\em Networks} 16 (1986) 295-317.

\item Wallace, S.W. \& Yan, T. :
Bounding Multi-Stage Stochastic Programs from Above,
{\em Mathematical Programming} 61 (1993) 111-129.

\item Wang, J. :
Continuity of the Feasible Solution Sets of Probabilistic Constrained Programs.
{\em Journal of Optimization and Applications} 63 (1989) 79-89.

\item Watanabe, T. \& Ellis, H. :
Robustness in Stochastic Programming Models,
{\em Appl. Math. Modelling} 17 (1993) 547-554.

\item Wets, R.J.B. :
Programming under Uncertainty : The Equivalent Convex Program.
{\em SIAM Journal of Applied Mathematics} 14 \#1 (1966) 89-105.

\item Wets, R.J.B. :
Programming under Uncertainty : The Solution Set.
{\em SIAM Journal of Applied Mathematics} 14 \#5 (1966) 1143-1151.

\item Wets, R.J.-B. :
Stochastic Programs with Fixed Recourse : The Equivalent Deterministic Program.
{\em SIAM Review} 16 (1974) 309-339.

\item Wets, R.J.-B. :
Solving Stochastic Programs with Simple Recourse.
{\em Stochastics} 10 (1983) 219-242.

\item Wets, R.J.-B. :
Challenges in Stochastic Programming,
{\em Mathematical Programming} 75 (1996) 115-135.

\item White, D.J. :
A Min-Max-Max-Min Approach to Solving a Stochastic Programming Problem
with Simple Recourse.
{\em Management Science} 38 (1992) 540-554.

\item Williams, A.C. :
A Stochastic Transpottation Problem,
{\em Operations Research} 11 (1963) 759-770.

\item Williams, A.C. :
On Stochastic Linear Programming,
{\em SIAM J. Appl. Math.} 13 (1965) 927-940.

\item Williams, A.C. :
Approximation Formulas for Stochastic Linear Programming,
{\em SIAM J. Appl. Math.} 14 (1966) 668-677.

\item Wright, S.E. :
Primal-Dual Aggregation and Disaggregation for Stochastic Linear Programs,
{\em Mathematics of Operation Research} 19 (1994) 893-908.

\begin{equation}{\label{v}}\tag{V}\mbox{}\end{equation}

Robust Optimization.

\item Adida, E. and Perakis, G.: (E-Article)
A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders,
{\em Mathematical Programming}, Ser. B, 107 (2006) 97-129.

\item Aghassi, M. and Bertsimas, D.:
Robust Game Theory,
{\em Mathematical Programming}, Ser. B (2006) 231-273.

\item Assavapokee, T., Realff, M.J. and Ammons, J.C.: (E-Article)
Min-Max Regret Robust Optimization Approach on Interval Data Uncertainty,
{\em Journal of Optimization Theory and Applications} 137 (2008) 297-316.

\item Averbakh, I.: (E-Article)
On the Complexity of a Class of Combinatorial Optimization Problems with Uncertainty,
{\em Mathematical Programming}, Ser. A, 90 (2001) 263-272.

\item Averbakh, I. and Zhao, Y.-B.: (E-Article)
Explicit Reformulations for Robust Optimization Problems with General Uncertainty Sets,
{\em SIAM Journal on Optimization} 18 (2008) 1436-1466.

\item Averbakh, I. and Zhao, Y.-B.:
Relaxed Robust Second-Order Cone Programming,
{\em Applied Mathematics and Computation} 210 (2009) 387-397.

\item Beck, A. and Ben-Tal, A.: (E-Article)
Duality in Robust Optimization: Primal Worst Equals Dual Best,
{\em Operations Research Letters} 37 (2009) 1-6.

\item Ben-Tal, A., Boyd, S. and Nemirovski, A.:
Extending Scope of Robust Optimization: Comprehensive Robust Counterpart of Uncertain Problems,
{\em Mathematical Programming}, Ser. B 107 (2006) 63-89.

\item Ben-Tal, A., Goryashko, A., Guslitzer, E. and Nemirovski, A.:
Adjustable Robust Solutions of Uncertain Linear Programs,
{\em Mathematical Programming}. Ser. A 99 (2004) 351-376.

\item Ben-Tal, A. and Nemirovski, A.:
Robust Convex Optimization,
{\em Mathematics of Operations Research} 23 (1998) 769-805.

\item Ben-Tal, A. and Nemirovski, A.:
Robust Solutions of Uncertain Linear Programs,
{\em Operations Research Letters} 25 (1999) 1-13.

\item Ben-Tal, A. and Nemirovski, A.:
Robust Solutions of Linear Programming Problems Contaminated with Uncertain Data,
{\em Mathematical Programming}. Ser. A 88 (2000) 411-424.

\item Ben-Tal, A. and Nemirovski, A.:
Robust Optimization: Methodology and Applications,
{\em Mathematical Programming}, Ser. B 107 (2002) 453-480.

\item Ben-Tal, A. and Nemirovski, A.: (E-Article)
Selected Topics in Robust Convex Optimization,
{\em Mathematical Programming}. Ser. B, 112 (2008) 125-158.

\item Ben-Tal, A., Nemirovski, A. and Roos, C.: (E-Article)
Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems,
{\em SIAM Journal on Optimization} 13 (2002) 535-560.

\item Bertsimas, D. and Brown, D.B.:
Constrained Stochastic LQC: A Tractable Approach,
{\em IEEE Trans. on Automatic Control} 52 (2007) 1826-1841.

\item Bertsimas, D., Natarajan, K. and Teo, C.-P.:
Persistence in Discrete Optimization under Data Uncertainty,
{\em Mathematical Programming} Ser. B, 108 (2006) 251-274.

\item Bertsimas, D. and Pachamanova:
Robust Multiperiod Portfolio Management in the Presence of Transaction Costs,
{\em Computers and Operations Research} 35 (2008) 3-17.

\item Bertsimas, D., Pachamanova, D. and Sim, M.:
Robust Linear Optimization under General Norms,
{\em Operations Research Letters} 32 (2004) 510-516.

\item Bertsimas, D. and Sim, M.: (E-Article)
Robust Discrete Optimization and Network Flows,
{\em Mathematical Programming} Ser. B, 98 (2003) 49-71.

\item Bertsimas, D. and Sim, M.:
The Price of Robustness,
{\em Operations Research} 52 (2004) 35-53.

\item Bertsimas, D. and Sim, M.: (E-Article)
Tractable Approximations to Robust Conic Optimization Problems,
{\em Mathematical Programming} Ser. B, 107 (2006) 5-36.

\item Bertsimas, D. and Thiele, A.: (E-Article)
A Robust Optimization Approach to Inventory Theory,
{\em Operations Research} 54 (2006) 150-168.

\item Beyer, H.-G. and Sendhoff, B.: (E-Article)
Robust Optimization — A Comprehensive Survey,
{\em Computer Methods in Applied Mechanics and Engineering} 196 (2007) 3190-3218.

\item Chen, X., Sim, M. and Sun, P.: (E-Article)
A Robust Optimization Perspective on Stochastic Programming,
{\em Operations Research} 55 (2007) 1058-1071.

\item El Ghaoui, L. and Lebret, H.:
Robust Solutions to Least-Squares Problems with Uncertain Data,
{\em SIAM Journal on Matrix Analysis and Applications} 18 (1997) 1035-1064.

\item El Ghaoui, L., Oustry, F. and Lebret, H.:
Robust Solutions to Uncertain Semidefinite Programs,
{\em SIAM Journal on Optimization} 9 (1998) 33-52.

\item Erdo\v{g}an, E. and Iyengar, G.: (E-Article)
Ambiguous Chance Constrained Problems and Robust Optimization,
{\em Mathematical Programming}, Ser. B 107 (2006) 37-61.

\item Goldfarb, D. and Iyengar, G.:
Robust Portfolio Selection Problems,
{\em Mathematics of Operations Research} 28 (2003) 1-38.

\item Goldfarb, D. and Iyengar, G.: (E-Article)
Robust Convex Quadratically Constrained Programs,
{\em Mathematical Programming} Ser. B, 28 (2003) 495-515.

\item Inuiguchi, M. and Sakawa, M.: (E-Article)
Robust Optimization under Softness in a Fuzzy Linear Programming Problem,
{\em International Journal of Approximate Reasoning} 18 (1998) 21-34.

\item Jung, D.H. and Lee, B.C.: (E-Article)
Development of a Simple and Efficient Method for Robust Optimization,
{\em International Journal for Numerical Methods in Engineering} 53 (2002) 2201-2215.

\item Mulvey, J.M., Vanderbei, R.J. and Zenios, S.A.: (E-Article)
Robust Optimization of Large-Scale Systems,
{\em Operations Research} 43 (1995) 264-281.

\item Perakis, G. and Sood, A.: (E-Article)
Competitive Multi-Period Pricing for Perishable Products: A Robust Optimization Approach,
{\em Mathematical Programming}, Ser. B 107 (2006) 295-335.

\item Schied, A.: (E-Article)
Risk Measures and Robust Optimization Problems,
{\em Stochastic Models} 22 (2006) 753-831.

\item Takriti, S. and Ahmed, S.: (E-Article)
On Robust Optimization of Two-Stage Systems,
{\em Mathematical Programming}, Ser. A, 99 (2004) 109-126.

\item Tuy, H.:
${\cal D}({\cal C})$-Optimization and Robust Global Optimization,
{\em Journal of Global Optimization} 47 (2010) 485-501.

\item Yang, D. and Zenios, S.A.: (E-Article)
A Scalable Parallel Interior Point Algorithm for Stochastic Linear Programming and Robust Optimization,
{\em Computational Optimization and Applications} 7 (1997) 143-158.

\item Yu, G.: (E-Article)
On the Max-Min 0-1 Knapsack Problem with Robust Optimization Applications,
{\em Operations Research} 44 (1996) 407-415.

\item Zhang, Y.: (E-Article)
General Robust Optimization Formulation for Nonlinear Programming,
{\em Journal of Optimization Theory and Applications} 132 (2007) 111-124.

\begin{equation}{\label{w}}\tag{W}\mbox{}\end{equation}

Neural Network for Optimization.

\item Abe, S., Kawakami, J. and Hirasawa, K.:
Solving Inequality Constrained Combinatorial Optimization Problems by the Hopfield Neural Netwroks,
{\em Neural Networks} 5 (1992) 663-670.

\item Bandler, J.W., Kellermann, W. and Madsen, K.:
A Nonlinear $L_{1}$ Optimization Algorithm for Design, Models, and Diagnosis of Networks,
{\em IEEE Trans. on Circuits and Systems} 34 (1987) 174-181.

\item Barnard, E.:
Optimization for Training Neural Nets,
{\em IEEE Trans. on Neural Networks} 3 (1992) 232-240.

\item Charalambous, C.:
A New Approach to Multicriterion Optimization Problem and Its Application
to the Design of 1-D Digital Filter,
{\em IEEE Trans. on Circuits and Systems} 36 (1989) 773-784.

\item Chua, L.O.:
Global Optimization: A Navie Approach,
{\em IEEE Trans. on Circuits and Systems} 37 (1990) 966-969.

\item Chua, L.O. and Lin, G.N.:
Nonlinear Optimization with Constraints: A Cook-Book Approach,
{\em International Journal of Circuit Theory and Applications} 11 (1983) 141-159.

\item Chua, L.O. and Lin, G.-N.:
Nonlinear Programming without Computation,
{\em IEEE Trans. on Circuits and Systems} 31 (1984) 182-188.

\item Cichocki, A. and Unbehauen, R.:
Switched-Capacitor Neural Networks for Differential Optimization,
{\em International Journal of Circuit Theory and Applications} 19 (1991)
161-187.

\item Cichocki, A. and Unbehauen, R.:
Neural Networks for Solving Systems of Linear Equations and Related Problems,
{\em IEEE Trans. on Circuits and Systems} 39 (1992) 124-138.

\item He, S., Reif, K. and Unbehauen, R.:
Multilayer Neural Networks for Solving a Class of Partial Differential
Equations,
{\em Neural Networks} 13 (2000) 385-396.

\item Huertas, J.L., Rueda, A., Rodriguez-Vazquez, A. and Chua, L.O.:
Canonical Nonlinear Programming Circuits,
{\em International Journal of Circuit Theory and Applications} 15 (1987) 71-77.

\item Jose, A.:
Definition of an Energy Function for Random Neural to Solve Optimization Problems,
{\em Neural Networks} 11 (1998) 731-737.

\item Kennedy, M.P. and Chua, L.O.:
Unifying the Tank and Hopfield Linear Programming Circuit and the Canonical
Nonlinear Programming Circuit of Chua and Lin,
{\em IEEE Trans. on Circuit and Systems} 34 (1987) 210-214.

\item Kennedy, M.P. and Chua, L.O.:
Neural Netwroks for Nonlinear Programming,
{\em IEEE Trans. on Circuits and Systems} 35 (1988) 554-562.

\item Maa, C.-Y. and Shanblatt, M.:
Linear and Quadratic Programming Neural Network Analysis,
{\em IEEE Trans. on Neural Networks} 3 (1992) 580-594.

\item Maa, C-Y. and Shanblatt, M.:
A Two-Phase Optimization Neural Network,
{\em IEEE Trans. on Neural Networks} 3 (1992) 1003-1009.

\item Osowski, S.:
Neural Network for Nonlinear Programming with Linear Equality Constraints,
{\em International Journal of Circuit Theory and Applications} 20 (1992) 93-98.

\item Rodr\'{i}guez-V\'{a}zquez, A., Dom\'{i}nguez-Castro, R., Rueda, A., Huertas, J.L. and S\'{a}nchez-Sinencio, E.:
Nonlinear Switched-Capacitor “Neural’ Networks for Optimization Problems,
{\em IEEE Trans. On Circuits and Systems} 37 (1990) 384-398.

\item Sexton, R.S., Dorsey, R.E. and Johnson, J.D.:
Optimization of Neural Networks: A Comparative Analysis of the Genetic
Algorithm and Simulated Annealing,
{\em European J. of Operational Research} 114 (1999) 589-601.

\item Shawe-Taylor, J.S. and Cohen, D.A.:
Linear Programming Algorithm for Neural Networks,
{\em Neural Networks} 3 (1990) 575-582.

\item Styblinski, M.A. and Tang, T.-S.:
Experiments in Nonconvex Optimization: Stochastic Approximation with
Function Smoothing and Simulated Annealing,
{\em Neural Networks} 3 (1990) 467-483.

\item Su, J., Hu, A. and He, Z.:
Solving a Knid of Nonlinear Programming Problems via Analog Neural Networks,
{\em Neurocomputing} 18 (1998) 1-9.

\item Sun, Y.:
A Generalized Updating Rule for Modified Hopfield Neural Network for
Quadratic Optimization,
{\em Neurocomputing} 19 (1998) 133-143.

\item Takahashi, Y.:
Generalization and Approximation Capabilities of Multilayer Networks,
{\em Neural Computation} 5 (1993) 132-139.

\item Takahashi, Y.:
Solving Dynamic Optimization Problems with Adaptive Networks,
{\em Neurocomputing} 25 (1999) 19-38.

\item Takahashi, Y.:
A Neural Network Theory for Constrained Optimization,
{\em Neurocomputing} 24 (1999) 117-161.

\item Tank, D.W. and Hopfield, J.J.:
Simple “Neural” Optimization Netwroks: An A/D Converter, Signal
Decision Circuit, and a Linear Programming Circuit,
{\em IEEE Trans. on Circuit and Systems} 33 (1986) 533-541.

\item Vandenberghe, L., de Moor, B.L. and Vandewalle, J.:
The Generalized Linear Complementarity Problem Applied to the Complete
Analysis of Resistive Piecewise-Linear Circuits,
{\em IEEE Trans. on Circuits and Systems} 36 (1989) 1382-1391.

\item Wang, J.:
A Deterministic Annealing Neural Network for Convex Programming,
{\em Neural Networks} 7 (1994) 629-641.

\item Wilson, G.:
Quadratic Programming Analogs,
{\em IEEE Trans. on Circuits and Systems} 33 (1986) 907-911.

\item Zhang, S. and Constantinides, A.G.:
Lagrange Programming Neural Networks,
{\em IEEE Trans. on Circuits and Systems — II: Analog and Digital Signal Processing} 39 (1992) 441-452.

\item Zhou, C.-S., Chen, T.-L. and Huang, W.-Q.:
Chaotic Neural Network with Nonlinear Self-Feedback and Its Application in Optimization,
{\em Neurocomputing} 14 (1997) 209-222.

\begin{equation}{\label{x}}\tag{X}\mbox{}\end{equation}

Vector Optimization.

\item Ad\'{a}n, M. and Novo, V.:
Optimality Conditions for Vector Optimization Problems with Generalized Convexity in Real Linear Spaces,
{\em Optimization} 51 (2002) 73-91.

\item Ad\'{a}n, M. and Novo, V.:
Efficient and Weak Efficient Points in Vector Optimization with Generalized Cone Convexity,
{\em Applied Mathematics Letters} 16 (2003) 221-225.

\item Antczak, T.:
An $\eta$-Approximation Method in Nonlinear Vector Optimization,
{\em Nonlinear Analysis} 63 (2005) 225-236.

\item Ballv\'{e}, M.E. and Guerra, P.J.:
Some Geometrical Aspects of the Efficient Line in Vector Optimization,
{\em European Journal of Operational Research} 162 (2005) 497-502.

\item Bigi, G. and Pappalardo, M.:
Regularity Conditions in Vector Optimization,
{\em Journal of Optimization Theory and Applications} 102 (1999) 83-96.

\item Cambini, A., Luc, D.T. and Martein, L.:
Order-Preserving Transformations and Applications,
{\em Journal of Optimization Theory and Applications} 118 (2003) 275-293.

\item Ceng, L.-C. and Yao, J.-C.:
Approximate Proximal Methods in Vector Optimization,
{\em European Journal of Operational Research} 183 (2007) 1-19.

\item Chen, G.-Y. and Craven, B.D. :
Existence and Continuity of Solutions for Vector Optimization,
{\em J. Optimization Theory and Applications} 81 (1994) 459-468.

\item Chen, G.-Y. and Rong, W.D.:
Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization,
{\em Journal of Optimization Theory and Applications} 98 (1998) 365-384.

\item Dauer, J.P. and Gallagher, R.J. :
Positive Proper Efficient Points and Related Cone Results in Vector Optimization Theory,
{\em SIAM J. Control and Optimization} 28 (1990) 158-172.

\item Dauer, J.P. and Stadler, W.:
A Survey of Vector Optimization in Infinite-Dimensional Spaces, Part 2,
{\em Journal of Optimization Theory and Applications} 51 (1986) 205-241.

\item Deng, S.:
On Approximate Solutions in Convex Vector Optimization,
{\em SIAM J. on Control and Optimization} 35 (1997) 2128-2136.

\item Deng, S.:
Characterizations of the Nonemptiness and Compactness of Solution Sets
in Convex Vector Optimization,
{\em Journal of Optimization Theory and Applications} 96 (1998) 123-131.

\item Deng, S.:
On Efficient Solutions in Vector Optimization,
{\em Journal of Optimization Theory and Applications} 96 (1998) 201-209.

\item Dentcheva, D. and Helbig, S. :
On Variational Principles, Level Sets, Well-Posedness, and $\epsilon$-Solutions
in Vector Optimization,
{\em J. Optimization Theory and Applications} 89 (1996) 325-349.

\item Durier, R.:
Weighting Factor Results in Vector Optimization,
{\em Journal of Optimization Theory and Applications} 58 (1988) 411-430.

\item Dutta, J. and Lalitha, C.S.:
Bounded Sets of KKT Multipliers in Vector Optimization,
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K-Epiderivatives for Set-Valued Functions and Optimization,
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Some Calculus Rules for Contingent Epiderivatives,
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\begin{equation}{\label{a1}}\tag{A1}\mbox{}\end{equation}

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