CONVEX ANALYSIS AND NONLINEAR OPTIMIZATION
J.M. Borwein and A.S. Lewis
Second Edition, Springer, New York, 2006. 310 pp. $74.95. eBook $54.99.
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
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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