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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.

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