Minimal convex functions bounded below by the duality product |
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Authors: | J.-E. Martí nez-Legaz B. F. Svaiter |
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Affiliation: | Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barce- lona, 08193 Bellaterra, Spain ; Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorinha 110, Jardim Botânico, Rio de Janeiro, CEP 22460-320, Brazil |
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Abstract: | It is well known that the Fitzpatrick function of a maximal monotone operator is minimal in the class of convex functions bounded below by the duality product. Our main result establishes that, in the setting of reflexive Banach spaces, the converse also holds; that is, every such minimal function is the Fitzpatrick function of some maximal monotone operator. Whether this converse also holds in a nonreflexive Banach space remains an open problem. |
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