Minimal convex functions bounded below by the duality product

Martínez-Legaz, J.-E.; Svaiter, B.

doi:10.1090/S0002-9939-07-09176-9

Minimal convex functions bounded below by the duality product
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by J.-E. Martínez-Legaz and B. F. Svaiter PDF

Proc. Amer. Math. Soc. 136 (2008), 873-878 Request permission

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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