Convex Functions: Constructions, Characterizations and Counterexamples

by Jonathan M. Borwein, Jon D. Vanderwerff

Overview

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

Product Details

ISBN-13:	9781139637282
Publisher:	Cambridge University Press
Publication date:	01/14/2010
Series:	Encyclopedia of Mathematics and its Applications , #109
Sold by:	Barnes & Noble
Format:	eBook
File size:	32 MB
Note:	This product may take a few minutes to download.

About the Author

Jonathan M. Borwein is Canada Research Chair in Distributed and Collaborative Research at Dalhousie University, Nova Scotia. He is presently Visiting Professor Laureate at the University of Newcastle, New South Wales.
Jon D. Vanderwerff is a Professor of Mathematics at La Sierra University, California.

Table of Contents

Preface; 1. Why convex?; 2. Convex functions on Euclidean spaces; 3. Finer structure of Euclidean spaces; 4. Convex functions on Banach spaces; 5. Duality between smoothness and strict convexity; 6. Further analytic topics; 7. Barriers and Legendre functions; 8. Convex functions and classifications of Banach spaces; 9. Monotone operators and the Fitzpatrick function; 10. Further remarks and notes; References; Index.

Editorial Reviews

"Borwein and Vanderwerff's book is particularly impressive due to its enormous breadth and depth. It is a beautiful experience to browse this inspiring book. The reviewer has not seen any source which is even close to presenting so many different and interesting convex functions and corresponding results. This delightful book is a most welcome addition to the library of any convex analyst or of any mathematician with an interest in convex functions."
Heinz H. Bauschke, Mathematical Reviews

"This masterful book emerges immediately as the de facto canonical source on it subject, and thus as a vital reference for students of Banach space geometry, functional analysis, analytic inequalities, and needless to say, any aspect of convexity. Truly then, anyone interested in nearly any branch of mathematical analysis should at least browse this book."
D.V. Feldman, Choice Magazine

From the Publisher