On the subdifferential of a saddle function
Copyright policy )On the subdifferential of a saddle function
AbstractLet K be a closed proper saddle function defined on the product Y × Z of two Banach spaces, at least one of which is reflexive. Two results about the Subdifferential ∂K of K are presented. The first asserts that the domain of ∂K is dense in the domain of K, a property which has been conjectured by R. T. Rockafellar. The second is concerned with the monotone operator TK: Y × Z → 2Y∗ × Z∗ associated with K: it is shown that TK has a unique maximal monotone extension to the bidual Y∗∗ × Z∗∗ and that TK is dense in this extension in a rather strong sense.
- University of Chicago United States
- Boston University Brussels Belgium
- Université Libre de Bruxelles Belgium
Monotone operators and generalizations, Convexity of real functions in one variable, generalizations, Analysis
Monotone operators and generalizations, Convexity of real functions in one variable, generalizations, Analysis
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