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

2025/11/02 by Abhik Digar, Digar, Abhik, Kuntal Som +1
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2511.00928

openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

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.

Citations

• Bilevel Programming Problems: A view through Set-valued Optimization
• A set optimization approach to zero-sum matrix games with multi-dimensional payoffs

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