Jonathan M. Borwein

"This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences," that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003"--Jacket.

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.

"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."--BOOK JACKET.

"The last twenty years have been witness to a fundamental shift in the way mathematics is practiced. With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians that can really take advantage of computer-aided research, especially given the scope and availability of modern computational packages such as Maple, Mathematica, and MATLAB. The authors provide a coherent variety of accessible examples of modern mathematics subjects in which intelligent computing plays a significant role."--BOOK JACKET.