A minmax theorem for concave-convex mappings with no regularity assumptions.

Abstract : We prove that zero-sum games with a concave-convex payoff mapping defined on a product of convex sets have a value as soon as the payoff mapping is bounded and one of the set is bounded and finite dimensional. In particular, no additional regularity assumption is required, such as lower or upper semicontinuity of the function or compactness of the sets. We provide several examples that show that our assumptions are minimal.
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Article dans une revue
Journal of Convex Analysis, Heldermann, 2015, 22 (2), pp.537-540
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Dernière modification le : lundi 29 mai 2017 - 14:21:54
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Perchet Vianney, Guillaume Vigeral. A minmax theorem for concave-convex mappings with no regularity assumptions.. Journal of Convex Analysis, Heldermann, 2015, 22 (2), pp.537-540. <hal-00927071>

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