Abstract Convex Analysis / Edition 1

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Overview

This book examines abstract convex analysis and presents the results of recent research, specifically on parametrizations of Minkowski type dualities and of conjugations of type Lau. It explains the main concepts through cases and detailed proofs.

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Editorial Reviews

Booknews
Presents a recent theory of abstract convex analysis that extends the concepts and results of conventional convex analysis to arbitrary sets and functions; provides many examples of applications of the general theory to sets, functions, conjugations, sub-differentials, and other areas; and demonstrates the applicability of various parts of the analysis to some topics in non-convex optimization. Most of the material is scattered in journals and collections, but some new results are also included. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Abstract Convexity of Elements of a Complete Lattice.

Abstract Convexity of Subsets of a Set.

Abstract Convexity of Functions on a Set.

Abstract Quasi-Convexity of Functions on a Set.

Dualities Between Complete Lattices.

Dualities Between Families of Subsets.

Dualities Between Sets of Functions.

Conjugations.

v-Dualities and _|_-Dualities.

Abstract Subdifferentials.

Notes and Remarks.

References.

Indexes.

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