On sufficiency and duality for nonsmooth multiobjective programming problems involving generalized V–rV–r-invex functions

In this paper, a class of nonsmooth multiobjective programming problems with inequality constraints is considered. We introduce the concepts of V–rV–r-pseudo-invex, strictly V–rV–r-pseudo-invex and V–rV–r-quasi-invex functions, in which the involved functions are locally Lipschitz. Based upon these generalized V–rV–r-invex functions, sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution are derived. Appropriate duality theorems are proved for a Mond–Weir-type dual program of a nonsmooth multiobjective programming under the aforesaid functions.