Optimality and Duality for Non-smooth Multiple Objective Semi-infinite Programming

The purpose of this paper is to consider a class of non-smooth multiobjective semi-infinite programming problem. Based on the concepts of local cone approximation, K − directional derivative and K − subdifferential, a new generalization of convexity, namely generalized uniform ( , , , ) K F d α ρ − − convexity, is defined for this problem. For such semi-infinite programming problem, several sufficient optimality conditions are established and proved by utilizing the above defined new classes of functions. The results extend and improve the corresponding results in the literature. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. Weak, strong and reverse duality theorems are also derived for Mond-Weir type multiobjective dual programs, using generalized invexity on the functions involved. Some previous duality results for differentiable multiobjective programming problems turn out to be special cases for the results described in the paper.