Convex Functions

Constructions, Characterizations and Counterexamples

AvJonathan M. Borwein,Jon D. Vanderwerff

Inbunden, Engelska, 2010

Del 109 i serien Encyclopedia of Mathematics and its Applications

1 999 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2010-01-14
Mått:156 x 234 x 28 mm
Vikt:920 g
Format:Inbunden
Språk:Engelska
Serie:Encyclopedia of Mathematics and its Applications
Antal sidor:532
Förlag:Cambridge University Press
ISBN:9780521850056
Utmärkelser:A Choice Outstanding Academic Title 2011

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.