Convex Functions

Convex Functions : Constructions, Characterizations and Counterexamples

5 (1 rating by Goodreads)
By (author)  , By (author) 

List price: US$125.00

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

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.show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 10 b/w illus. 640 exercises
  • 1139087320
  • 9781139087322

Review quote

'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.' Choiceshow more

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.show more

About Jonathan M. Borwein

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.show more

Rating details

1 ratings
5 out of 5 stars
5 100% (1)
4 0% (0)
3 0% (0)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X