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.
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