J.M. Borwein and A.S. Lewis

Second Edition, Springer, New York, 2006. 310 pp. $74.95. eBook $54.99. ISBN 978-0-387-29570-1

This book is a concise account of convex analysis, its applications and extensions, for a broad audience. Blurring as it does the distinctions between mathematical optimization and modern analysis, the elegant language of convexity and duality is indispensable both in computational optimization and for understanding variational properties of functions and multifunctions.

Primarily aimed at first-year graduate students, the text consists of short, self-contained sections, each followed by an extensive set of exercises, many of which are guided. The book is thus appropriate either as a class text or for self study.

Contents: Background.- Inequality constraints.- Fenchel duality.- Convex analysis.- Special cases.- Nonsmooth optimization.- The Karush-Kuhn-Tucker Theorem.- Fixed points.- More nonsmooth structure.- Postscript: infinite versus finite dimensions.

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