Existence of Weak Efficient Solutions of Set-Valued Optimization Problems

TL;DR

This paper introduces a new scalarization function for set-valued maps to establish Weierstrass-type theorems in noncontinuous set optimization problems, enhancing existing theoretical results.

Contribution

It proposes a novel scalarization approach that improves upon previous results in set-valued optimization theory.

Findings

Established new Weierstrass-type theorems for noncontinuous set optimization.

Demonstrated the effectiveness of the scalarization function under coercivity conditions.

Extended the theoretical framework of set-valued optimization problems.

Abstract

In this paper, we consider a new scalarization function for set-valued maps. As the main goal, by using this scalarization function, we obtain some Weierstrass-type theorems for the noncontinuous set optimization problems via the coercivity and noncoercivity conditions. This contribution improves various existing results in the literature.