Sequential optimality conditions and solution existence for nonsmooth multiobjective optimization problems

Abstract

In this paper, we consider a multiobjective optimization problem, where its feasibility set is unbounded and the related functions are nonsmooth and nonconvex. We first present new sequential necessary/sufficient optimality conditions that are established in terms of asymptotic value sets for weak Pareto solutions and weak Pareto values of the considered problem. We then examine how asymptotic values and Karush–Kuhn–Tucker values guarantee the existence of different types of Pareto solutions of the underlying problem. To achieve these goals, we utilize the tool of variational analysis to define sets of asymptotic values and Karush–Kuhn–Tucker values of the multiobjective optimization problem.