Robust Optimality and Duality in Multiobjective Optimization Problems under Data Uncertainty

Abstract

In this paper, we employ advanced techniques of variational analysis and generalized differentiation to examine robust optimality conditions and robust duality for an uncertain nonsmooth multiobjective optimization problem under arbitrary uncertainty nonempty sets. We establish necessary and sufficient optimality conditions for (local) robust (weakly) efficient solutions of the considered problem. Our problem involves nonsmooth real-valued functions and data uncertainty in both the objective and constraint functions, and its necessary and sufficient optimality conditions are exhibited in terms of multipliers and the Mordukhovich or Clarke subdifferentials of the related functions. Moreover, we formulate a dual multiobjective problem to the underlying program and examine robust weak, strong, and converse duality relations between the primal problem and its dual under assumptions of (strictly) generalized convexity.