Strong Second-Order Karush--Kuhn--Tucker Optimality Conditions for Vector Optimization

TL;DR

This paper develops strong second-order KKT optimality conditions for vector optimization problems with inequality constraints, using advanced second-order differential tools to improve understanding of optimality in such problems.

Contribution

It introduces new second-order regularity conditions and establishes strong second-order KKT necessary conditions for Geoffrion properly efficient solutions in vector optimization.

Findings

Established second-order KKT conditions for vector optimization.

Introduced second-order regularity conditions based on symmetric subdifferential.

Provided examples illustrating the theoretical results.

Abstract

In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open set. By using the second-order symmetric subdifferential and the second-order tangent set, we propose two types of second-order regularity conditions in the sense of Abadie. Then we establish some strong second-order Karush--Kuhn--Tucker necessary optimality conditions for Geoffrion properly efficient solutions of the considered problem. Examples are given to illustrate the obtained results.