Overview

Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.

Full Product Details

Author:   Jonathan Borwein ,  Adrian S. Lewis
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 2nd ed. 2006
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.498kg
ISBN:  

9781441921277

ISBN 10:   1441921273
Pages:   310
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Background.- Inequality Constraints.- Fenchel Duality.- Convex Analysis.- Special Cases.- Nonsmooth Optimization.- Karush—Kuhn—Tucker Theory.- Fixed Points.- More Nonsmooth Structure.- Postscript: Infinite Versus Finite Dimensions.- List of Results and Notation.

Reviews

From the reviews: MATHEMATICAL REVIEWS The present book gives a concise treatment of the area, aiming to show the relevance in particular of new developments in nonsmooth analysis to optimization theory...The book is of a manageable size and as such should appeal to the student. Further, the proofs are generally short and snappy, revealing the power of the abstract structural approach and fruitful interplay of geometrical and topological ideas. However, considerable ground is covered and, as a graduate text should, it develops the subject up to the frontiers of current research, giving an idea of areas for further exploration...This text will give impetus to the teaching of analysis because it makes evident its significant applications in optimization. But it will also bring added attraction to the study of optimization because it reveals so much of its abstract structural base. The book is divided into 11 chapters and provides a comprehensive presentation of the main features of convex analysis and nonlinear optimisation. Each result is sustained by a set of theorems, propositions and corollaries and includes rigorous proofs and clarifying discussions. They are complemented by a series of theoretical exercises. ... This book is warmly recommended for an advanced course in analysis for mathematicians or as a first graduate course for students involved with optimization theory. (Carlos Narciso Bouza Herrera, Zentralblatt MATH, Vol. 1116 (18), 2007)

From the reviews: MATHEMATICAL REVIEWS The present book gives a concise treatment of the area, aiming to show the relevance in particular of new developments in nonsmooth analysis to optimization theory!The book is of a manageable size and as such should appeal to the student. Further, the proofs are generally short and snappy, revealing the power of the abstract structural approach and fruitful interplay of geometrical and topological ideas. However, considerable ground is covered and, as a graduate text should, it develops the subject up to the frontiers of current research, giving an idea of areas for further exploration!This text will give impetus to the teaching of analysis because it makes evident its significant applications in optimization. But it will also bring added attraction to the study of optimization because it reveals so much of its abstract structural base. The book is divided into 11 chapters and provides a comprehensive presentation of the main features of convex analysis and nonlinear optimisation. Each result is sustained by a set of theorems, propositions and corollaries and includes rigorous proofs and clarifying discussions. They are complemented by a series of theoretical exercises. ! This book is warmly recommended for an advanced course in analysis for mathematicians or as a first graduate course for students involved with optimization theory. (Carlos Narciso Bouza Herrera, Zentralblatt MATH, Vol. 1116 (18), 2007)

Aus den Rezensionen zur 2. Auflage: Das vorliegende Werk bietet eine anspruchsvolle Einfuhrung in die nichtlineare Optimierung in endlichdimensionalen Raumen. ! Die Autoren haben einige bemerkenswerte Entscheidungen bei der Zusammenstellung dieses Werkes getroffen. ! Der Stil ist informell, die Kapitel sind nur lose aufeinander aufbauend, es ist also nicht unbedingt erforderlich, das Buch von vorn nach hinten durchzuarbeiten. Dies macht es auch fur fortgeschrittene Studentinnen und Studenten attraktiv. (F. Rendl, in: IMN - Internationale Mathematische Nachrichten, 2008, Issue 207, S. 50)

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