Nondifferentiable multiobjective programming under generalized image-invexity

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of dIdI-invexity and generalized dIdI-invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction didi. New Fritz–John type necessary and Karush–Kuhn–Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient, efficient or properly efficient. Moreover, we prove weak, strong, converse and strict duality results for a Mond–Weir type dual under various types of generalized dIdI-invexity assumptions.