Sufficient optimality conditions and duality in nonsmooth multiobjective optimization problems under generalized convexity

Abstract

We consider a multiobjective optimization problem in ℝn with a feasible set defined by inequality and equality constraints and a set constraint. All the involved functions are, at least, directionally differentiable. We provide sufficient optimality conditions for global and local Pareto minimum under several kinds of generalized convexity. Also Wolfe-type and Mond-Weir-type dual problems are considered, and weak and strong duality theorems are proved. © 2006 Springer-Verlag Berlin Heidelberg.