Abstract
This paper aims to present alternative characterizations for different types of set-valued robustness concepts. Equivalent scalar representations for various set order relations are derived when the sets are the union of sets. Utilizing these findings in conjunction with image space analysis, specific isolated sets are defined for different notions of robust solutions. These isolated sets serve as the basis for deriving both necessary and sufficient robust optimality conditions. The validity of the results is demonstrated through several illustrative examples. Additionally, the paper concludes with an application of our present approach to two-player zero-sum matrix games.
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The authors are grateful to the Editor-in-Chief and the anonymous referee for their valuable comments and suggestions, which improved the presentation of the paper.
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Communicated by Christiane Tammer.
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Das, M., Nahak, C. & Biswal, M.P. Treatment of Set-Valued Robustness via Separation and Scalarization. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02423-4
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DOI: https://doi.org/10.1007/s10957-024-02423-4