Remarks on the paper "Treatment of Set-Valued Robustness via Separation and Scalarization"

TL;DR

This paper critically reviews and corrects previous work on set-valued robust optimization, introduces new concepts of robust solutions, and enhances scalarization methods for uncertain set-valued problems.

Contribution

It identifies inconsistencies in prior results, provides corrected and improved theorems, and introduces new concepts for robust solutions in set-valued optimization.

Findings

Corrected previous results on set-valued robustness

Introduced new concepts of robust solutions

Enhanced scalarization methods for set-valued problems

Abstract

In this paper, we remark on the published paper "Treatment of Set-Valued Robustness via Separation and Scalarization" [1], which deals with the robust solution to an uncertain constrained set-valued optimization problem via scalarization methods. We show many inconsistencies in the results of the above-mentioned paper. We improve most of these results. In the process, we introduce some new concepts of robust solutions for uncertain set-valued optimization problems. We also improve some results on scalarization methods applicable to set-valued optimization.