On AKKT optimality conditions for cone-constrained vector optimization problems

TL;DR

This paper introduces an approximate KKT condition (AKKT) for cone-constrained vector optimization, establishing its necessity and sufficiency under various conditions, and explores related constraint qualifications.

Contribution

It proposes a new AKKT condition for cone-constrained vector optimization and analyzes its necessity and sufficiency without constraint qualifications.

Findings

AKKT is necessary for local weak efficient solutions without constraint qualification.

For convex problems, AKKT is both necessary and sufficient for global weak efficiency.

The paper introduces strict constraint qualifications related to AKKT.

Abstract

In this paper, we introduce a kind of approximate Karush--Kuhn--Tucker condition (AKKT) for a smooth cone-constrained vector optimization problem. We show that, without any constraint qualification, the AKKT condition is a necessary for a local weak efficient solution of the considered problem. For convex problems, we prove that the AKKT condition is a necessary and sufficient optimality condition for a global weak efficient solution. We also introduce some strict constraint qualifications associated with the AKKT condition.