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Minimax Theory and its Applications 09 (2024), No. 2, 377--388 Copyright Heldermann Verlag 2024 Generalized Characterization Theorems for Set Relations and an Application to Multi-Valued Optimization Yuto Ogata Kanazawa Gakuin University, Ishikawa, Japan y-ogata@kanazawa-gu.ac.jp This paper proposes relaxed characterization for set relations by scalarization functions and states a generalized Gordan's theorem of the alternative for set-valued maps. As an application, we introduce some robustness of multi-valued optimization problems together with an algorithm by which its criteria can be calculated. Keywords: Set optimization, set relation, scalarization, theorem of the alternative, robustness. MSC: 90C46, 90C29, 49J53. [ Fulltext-pdf (113 KB)] for subscribers only. |