Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weir-type dual problems for our nonsmooth multiobjective problems and establish duality theorems for (weak) Pareto-optimal solutions under generalized convexity assumptions and regularity conditions.