Convex Functions
Constructions, Characterizations and Counterexamples
Published on 14. January 2010
Book
Hardback
532 pages
978-0-521-85005-6 (ISBN)
Description
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.
Reviews / Votes
'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 beautiful 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 its subject, and thus as a vital reference for students ... In the exercises and asides, which maintain lively rapport with a spectrum of mathematical concerns, one finds mention of unexpected topics such as the brachistochrone problem and the Riemann zeta function.' ChoiceMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 10 Halftones, unspecified
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 33 mm
Weight
957 gr
ISBN-13
978-0-521-85005-6 (9780521850056)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Jonathan M. Borwein | Jon D. Vanderwerff
Convex Functions
Constructions, Characterizations and Counterexamples
E-Book
05/2012
Cambridge University Press
€133.99
Available for download
E-Book
01/2010
Cambridge University Press
€111.99
Available for download
Persons
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.
Content
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.