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<p>The purpose of this paper is to derive the equivalent characterizations of the robust solutions for the uncertain set-valued optimization problems, encompassing various notions of robustness. We derive the equivalent representations of the binary relations when the sets are the union of the sets. Subsequently, using the extended signed distances, we obtain the equivalent scalar characterizations of the same. Based on the scalarization results for different binary relations and employing image space analysis, we construct appropriate subsets in the scalarization image space for different binary relations to establish robust optimality conditions. Our method doesn’t need the convexity assumption of the sets. The practical validity of our findings is demonstrated through the presentation of multiple illustrative examples. Finally, we apply our results to two-person zero-sum matrix games characterized by multidimensional payoffs.</p>

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Characterization of set-valued robustness via extended signed distances and separation

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Madhusudan Das,
  • C. Nahak

摘要

The purpose of this paper is to derive the equivalent characterizations of the robust solutions for the uncertain set-valued optimization problems, encompassing various notions of robustness. We derive the equivalent representations of the binary relations when the sets are the union of the sets. Subsequently, using the extended signed distances, we obtain the equivalent scalar characterizations of the same. Based on the scalarization results for different binary relations and employing image space analysis, we construct appropriate subsets in the scalarization image space for different binary relations to establish robust optimality conditions. Our method doesn’t need the convexity assumption of the sets. The practical validity of our findings is demonstrated through the presentation of multiple illustrative examples. Finally, we apply our results to two-person zero-sum matrix games characterized by multidimensional payoffs.