Approximate solutions in multiobjective interval-valued optimization problems: Existence theorems and optimality conditions

TL;DR

This paper investigates approximate solutions in multiobjective interval-valued optimization, establishing existence theorems and optimality conditions, including KKT conditions, for nonsmooth, nonconvex problems, with applications to game theory.

Contribution

It introduces new existence theorems and KKT optimality conditions for approximate solutions in complex multiobjective interval-valued problems.

Findings

Proved existence of approximate solutions under mild conditions.

Derived KKT optimality conditions for nonsmooth, nonconvex problems.

Applied results to a multiobjective game scenario.

Abstract

This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some mild conditions. Moreover, we give KKT optimality conditions for approximate solutions for such a problem whose associated functions are nonsmooth and nonconvex. We also propose the approximate KKT optimality condition of an approximate solution for such a problem. Finally, we apply some obtained results to a noncooperative game involving the multiobjective interval-valued function.