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Partially Ball Weakly Inf-Compact Saddle Functions

Université Montpellier II, Département de Mathématiques, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
Section of Operations Research, Department of Mathematics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria, and Université Montpellier II, Département de Mathématiques, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
thibault{at}math.univ-montp2.fr
zlateva{at}fmi.uni-sofia.bg
zlateva{at}math.univ-montp2.fr

We study on a product Banach space the properties of a class of saddle functions called partially ball weakly inf-compact. For such a function we prove that the domain of the subdifferential is nonempty, that the operator naturally associated with the subdifferential is maximal monotone, and that the subdifferential of the function is integrable. For a function in a large subclass of that class we prove the density of the domain of the subdifferential in the domain of the function.

Key Words: saddle function; subdifferential; integrability; maximal monotone operator
History: Received: September 30, 2003; revision received: June 18, 2004;