Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions

TL;DR

This paper develops second-order optimality conditions for constrained vector optimization problems with locally Lipschitz functions, introducing new constraint qualifications and regularity conditions in a nonsmooth setting.

Contribution

It proposes new second-order constraint qualifications and regularity conditions for nonsmooth vector optimization, linking them to KKT conditions for local solutions.

Findings

Established connections between various second-order constraint qualifications.

Derived second-order KKT necessary conditions for local efficient solutions.

Provided examples illustrating the theoretical results.

Abstract

In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint qualifications of Zangwill type, Abadie type and Mangasarian~--~Fromovitz type as well as a regularity condition of Abadie type are proposed in a nonsmooth setting. The connections between these proposed conditions are established. They are applied to develop second-order Karush--Kuhn--Tucker necessary optimality conditions for local (weak, Geoffrion properly) efficient solutions to the considered problem. Examples are also given to illustrate the obtained results.