Duality in nondifferentiable minimax fractional programming with B-(p, r)- invexity

In this article, we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution to the problem and then establish weak, strong, and strict converse duality theorems for the problem and its dual problem under B-(p, r)-invexity assumptions. Examples are given to show that B-(p, r)-invex functions are generalization of (p, r)-invex and convex functionsAMS Subject Classification: 90C32; 90C46; 49J35.

[1]  Majid Soleimani-Damaneh,et al.  Infinite (semi-infinite) problems to characterize the optimality of nonlinear optimization problems , 2008, Eur. J. Oper. Res..

[2]  J. C. Lee,et al.  On duality theorems for a nondifferentiable minimax fractional programming , 2002 .

[3]  R. N. Mukherjee,et al.  Duality for fractional minimax programming problems , 1990, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[4]  Majid Soleimani-damaneh,et al.  Generalized invexity in separable Hilbert spaces , 2009 .

[5]  B. Mordukhovich Variational Analysis and Generalized Differentiation II: Applications , 2006 .

[6]  Optimality Conditions and Duality in Nonsmooth Multiobjective Programs , 2010 .

[7]  B. Mond,et al.  Generalized fractional programming duablity: a ratio game approach , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[8]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[9]  Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions , 2010 .

[10]  M. A. Hanson On sufficiency of the Kuhn-Tucker conditions , 1981 .

[11]  Do Sang Kim,et al.  Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming , 2010 .

[12]  S. Chandra,et al.  Duality in fractional minimax programming , 1995, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[13]  Shinji Tanimoto Duality for a class of nondifferentiable mathematical programming problems , 1981 .

[14]  Kensuke Tanaka,et al.  Necessary and sufficient conditions for minimax fractional programming , 1999 .

[15]  Majid Soleimani-Damaneh,et al.  Nonsmooth Optimization Using Mordukhovich's Subdifferential , 2009, SIAM J. Control. Optim..

[16]  Xinmin Yang,et al.  Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems , 2010 .

[17]  Brahim Aghezzaf,et al.  Generalized Invexity and Duality in Multiobjective Programming Problems , 2000, J. Glob. Optim..

[18]  B. Craven Invex functions and constrained local minima , 1981, Bulletin of the Australian Mathematical Society.

[19]  Tadeusz Antczak,et al.  Generalized fractional minimax programming with B-(p, r)-invexity , 2008, Comput. Math. Appl..

[20]  Juan J. Nieto,et al.  Nonsmooth multiple-objective optimization in separable Hilbert spaces , 2009 .

[21]  W. Schmitendorf Necessary conditions and sufficient conditions for static minmax problems , 1977 .