Nondifferentiable multiobjective programming under generalized dl-invexity

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of d(l)-invexity and generalized d(l)-invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d(l) 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 d(l)-invexity assumptions. (C) 2009 Elsevier B.V. All rights reserved.