On semi-G-V -type I concepts for directionally differentiable multiobjective programming problems

Abstract

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V -type I objective andconstraint functions and their generalizations are introduced for such nonsmooth vector optimizationproblems. Based upon these generalized invex functions, necessary and sufficient optimality conditionsare established for directionally differentiable multiobjective programming problems. Thus, new FritzJohn type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considereddirectionally differentiable multiobjective programming problem. Further, weak, strong and converseduality theorems are also derived for Mond-Weir type vector dual programs.