A note on approximate Karush-Kuhn-Tucker conditions in locally Lipschitz multiobjective optimization

TL;DR

This paper extends approximate KKT conditions to locally Lipschitz multiobjective optimization problems using Mordukhovich subdifferentials, establishing necessary and sufficient optimality conditions and linking AKKT to KKT under certain conditions.

Contribution

It introduces a generalized AKKT framework for nonsmooth multiobjective problems and connects it to classical KKT conditions.

Findings

Extended AKKT conditions to locally Lipschitz functions.

Proved AKKT implies KKT under additional assumptions.

Provided necessary and sufficient optimality conditions.

Abstract

In the recent paper of Giorgi, Jim\'enez and Novo (J Optim Theory Appl 171:70--89, 2016), the authors introduced the so-called approximate Karush-Kuhn-Tucker (AKKT) condition for smooth multiobjective optimization problems and obtained some AKKT-type necessary optimality conditions and sufficient optimality conditions for weak efficient solutions of such a problem. In this note, we extend these optimality conditions to locally Lipschitz multiobjective optimization problems using Mordukhovich subdifferentials. Furthermore, we prove that, under some suitable additional conditions, an AKKT condition is also a KKT one.