Treatment of Set-Valued Robustness via Separation and Scalarization

Madhusudan Das, Chandal Nahak () and Mahendra Prasad Biswal
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Madhusudan Das: Indian Institute of Technology
Chandal Nahak: Indian Institute of Technology
Mahendra Prasad Biswal: Indian Institute of Technology

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 2, No 13, 843-865

Abstract: 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.

Keywords: Robustness; Uncertain set-valued optimization; Image space analysis; Set relations; 49J53; 49N30; 54C60; 90C31 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02423-4

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