Abstract
We consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a compact convex set. We introduce G-Karush-Kuhn-Tucker conditions and G-Fritz John conditions for our nondifferentiable multiobjective programs. By using suitable G-invex functions, we establish G-Karush-Kuhn-Tucker necessary and sufficient optimality conditions, and G-Fritz John necessary and sufficient optimality conditions of our nondifferentiable multiobjective programs. Our optimality conditions generalize and improve the results in Antczak (2009) to the nondifferentiable case.
Highlights
Introduction and PreliminariesA number of different forms of invexity have appeared
Based on the paper by Mond and Schechter, Yang et al studied a class of nondifferentiable multiobjective programs. They replaced the objective function by the support function of a compact convex set, constructed a more general dual model for a class of nondifferentiable multiobjective programs, and established only weak duality theorems for efficient solutions under suitable weak convexity conditions
Antczak 13, 14 studied the optimality and duality for G-multi-objective programming problems. They defined a new class of differentiable nonconvex vector valued functions, namely, the vector G-invex G-incave functions with respect to η
Summary
A number of different forms of invexity have appeared. In 1 , Martin defined Kuhn-Tucker invexity and weak duality invexity. Craven and Glover 5 established Kuhn-Tucker type optimality conditions for cone invex programs, and Jeyakumar and Mond 6 introduced the class of the so-called V-invex functions to proved some optimality for a class of differentiable vector optimization problems than under invexity assumption. Egudo 7 established some duality results for differentiable multiobjective programming problems with invex functions. Based on the paper by Mond and Schechter , Yang et al studied a class of nondifferentiable multiobjective programs. They replaced the objective function by the support function of a compact convex set, constructed a more general dual model for a class of nondifferentiable multiobjective programs, and established only weak duality theorems for efficient solutions under suitable weak convexity conditions.
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