Optimality conditions for approximate Pareto solutions of a nonsmooth vector optimization problem with an infinite number of constraints

TL;DR

This paper develops new necessary and sufficient optimality conditions using Clarke subdifferentials for approximate Pareto solutions in nonsmooth vector optimization problems with infinitely many constraints, including special cases.

Contribution

It introduces novel optimality conditions for complex nonsmooth, infinite-constraint vector optimization problems, extending existing theory.

Findings

Derived Clarke subdifferential-based optimality conditions

Applied conditions to cone-constrained convex and semidefinite problems

Provided illustrative examples demonstrating the results

Abstract

In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints. As a consequence, we obtain optimality conditions for the particular cases of cone-constrained convex vector optimization problems and semidefinite vector optimization problems. Examples are given to illustrate the obtained results.