1. Fenchel–Moreau conjugation for lower semi-continuous functions.
- Author
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Cotrina, John, Karas, Elizabeth W., Ribeiro, Ademir A., Sosa, Wilfredo, and Yuan, Jin Y.
- Subjects
- *
CONJUGATE gradient methods , *CONTINUOUS functions , *CONVEX functions , *DUALITY theory (Mathematics) , *TOPOLOGICAL spaces , *MATHEMATICAL optimization - Abstract
We introduce a modification of Fenchel's conjugation which is a particular case of Moreau's conjugation. We obtain good properties such as convexity of the conjugate function even though the function is not convex. We also introduce the concept of conjugate dual space as a class of continuous operators, while in the Fenchel conjugation the conjugate dual space is the classical topological dual space. Finally, we present some examples for illustrating the difference between the Fenchel–Moreau conjugation and our modification. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
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