Optimality conditions at infinity for nonsmooth minimax programming

TL;DR

This paper develops necessary and sufficient optimality conditions at infinity for nonsmooth minimax programming problems using limiting subdifferential and normal cone concepts, with applications to vector optimization.

Contribution

It introduces a novel approach to derive KKT-type optimality conditions at infinity for nonsmooth minimax problems, extending existing theory.

Findings

Derived KKT-type conditions at infinity for nonsmooth minimax problems

Applied the results to nonsmooth vector optimization

Provided a framework for analyzing optimality at infinity in nonsmooth settings

Abstract

This paper is devoted to study of optimality conditions at infinity in nonsmooth minimax programming problems and applications. By means of the limiting subdifferential and normal cone at infinity, we dirive necessary and sufficient optimality conditions of Karush--Kuhn--Tucker type for nonsmooth minimax programming problems with constraint. The obtained results are applied to a nonsmooth vector optimization problem.