Deterministic characterizations of approximate solutions for nonsmooth nonconvex uncertain programs

Abstract

The main purpose of this paper is to study a nonsmooth vector programming problem affected by data uncertainty. The partial ordering in objective image space is induced by a proper cone lying in $n-$dimensional Euclidean space. The Clarke's generalized subgradients and generalized pseudoquasi-convexity assumptions are used to extract Pareto efficient solutions. Then Karush-Kuhn-Tucker (KKT) optimality conditions over cones and the generalized convexity assumptions are employed to find a Primal-Dual relationship between the uncertainty problem and a Mond-Weir type dual. Lastly, a generalized Lagrangian function is introduced, and the feasible solutions of the data uncertainty problem are characterized in terms of saddle points of the Lagrangian function.