Duality for Nonconvex Approximation and Optimization / Edition 1

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Overview

In this monograph the author presents the theory of duality for nonconvex approximation in normed linear spaces and nonconvex global optimization in locally convex spaces. Detailed proofs of results are given, along with varied illustrations. While many of the results have been published in mathematical journals, this is the first time these results appear in book form. In addition, unpublished results and new proofs are provided. This monograph should be of great interest to experts in this and related fields.
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Editorial Reviews

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From the reviews:

"Being the first monograph devoted to nonconvex duality, this book is going to become a fundamental source for researchers in the field. An important feature of the book is that it is also accessible to nonspecialists, since, in spite of dealing with a rather specialized topic, it is essentially self-contained. … this monograph is a very useful addition to the existing literature on optimization and approximation and is undoubtedly going to constitute a major reference on nonconvex duality." (Juan-Enrique Martinez-Legaz, Mathematical Reviews, Issue 2006 k)

"This monograph, being the first book of this kind in the literature, covers a wide range of optimization and approximation problems. It provides an excellent overview over the literature and, moreover, it contains a lot of new results and new proofs of known results. The results and the choice of the classes of problems are well motivated. … The monograph is appropriate for graduate students and advanced readers." (Andreas Löhne, Mathematical Methods of Operations Research, Vol. 66, 2007)

"In this monograph the author presents some approaches to duality in nonconvex approximation in normed linear spaces and to duality in nonconvex global optimization in locally convex spaces. … It is my belief that the monograph under review will become a fundamental reference on nonconvex duality for researchers in the field, and, although the topics are very specialized, the monograph is also accessible to nonspecialists … . is strongly recommended to researchers, postgraduate and graduate students interested in nonconvex duality theory." (Fabián Flores Bazán, Zentralblatt MATH, Vol. 1119 (21), 2007)

"This is a nice addition to the literature on nonconvex optimization in locally convex spaces, devoted primarily to nonconvex duality. Most of the material appears for the first time in book form and examples are abundant. … The style is friendly. I strongly recommend this book to graduate students studying nonconvex optimization theory." (Constantin P. Niculescu, Revue Roumaine de Mathématique Pures et Appliquées, Vol. LII (5), 2007)

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Product Details

  • ISBN-13: 9780387283944
  • Publisher: Springer New York
  • Publication date: 2/16/2006
  • Series: CMS Books in Mathematics Series
  • Edition description: 2006
  • Edition number: 1
  • Pages: 356
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

1 Preliminaries 1
2 Worst approximation 85
3 Duality for quasi-convex supremization 101
4 Optimal solutions for quasi-convex maximization 137
5 Reverse convex best approximation 153
6 Unperturbational duality for reverse convex infimization 169
7 Optimal solutions for reverse convex infimization 203
8 Duality for D.C. optimization problems 213
9 Duality for optimization in the framework of abstract convexity 259
10 Notes and remarks 279
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