Ivan Singer

Duality for Nonconvex Approximation and Optimization (eBook, PDF)

• Format: PDF

Produktbeschreibung

The theory of convex optimization has been developing constantly over the past 30 years. Recently, researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimization problems. This monograph contains an exhaustive presentation of the duality theory for these classes of problems and their generalizations.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 356
• Erscheinungstermin: 12. März 2007
• Englisch
• ISBN-13: 9780387283951
• Artikelnr.: 37286918

Autorenporträt

The theory of convex optimization has been developing constantly over the past 30 years. Recently, researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimization problems. This monograph contains an exhaustive presentation of the duality theory for these classes of problems and their generalizations.

Inhaltsangabe

Preliminaries.- Worst Approximation.- Duality for Quasi-convex Supremization.- Optimal Solutions for Quasi-convex Maximization.- Reverse Convex Best Approximation.- Unperturbational Duality for Reverse Convex Infimization.- Optimal Solutions for Reverse Convex Infimization.- Duality for D.C. Optimization Problems.- Duality for Optimization in the Framework of Abstract Convexity.- Notes and Remarks.

Rezensionen

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 stronglyrecommend this book to graduate students studying nonconvex optimization theory." (Constantin P. Niculescu, Revue Roumaine de Mathématique Pures et Appliquées, Vol. LII (5), 2007)