On optimality conditions and duality results for a new class of nonconvex nondifferentiable multicriteria optimization problems

Abstract

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with both inequality and equality constraints is considered. Namely, the sufficient optimality conditions and Mond-Weir duality results are established for such nondifferentiable multicriteria optimization problems in which the involved functions are nondifferentiable (b,,,)^{w}-univex functions (not necessarly with respect to the same functions b and  and the same ). Then the aforesaid results developed here under (b,,,)^{w}-uinvexity are applicable for a larger class of nonsmooth vector optimization problems than under other generalized convexity notions existing in the literature.