Convex Analysis and Monotone Operator Theory in Hilbert Spaces (CMS Books in Mathematics)
| Author | : | |
| Rating | : | 4.41 (694 Votes) |
| Asin | : | 1461428696 |
| Format Type | : | paperback |
| Number of Pages | : | 468 Pages |
| Publish Date | : | 2017-09-26 |
| Language | : | English |
DESCRIPTION:
A modern treatment of convex analysis—complete with operator splitting methods Bauschke and Combettes provide a timely addition to the literature on convex analysis and optimization. The first section of the book covers the necessary background topics (Hilbert spaces, basic analysis of convex sets/functions, fixed-point theorems, etc.).From here, the book moves into conjugacy, duality, and (sub)differentiability, covering infimal convolution, proximal operators, and other "tools" along the way.The text then moves on to monotone operators, covering the basic definitions and ideas before diving into resolvents, sums, and zeros of monotone operators. Wi
The book is accessible to a broad audience, and reaches out in particular to applied scientists and engineers, to whom these tools have become indispensable.. A concise exposition of related constructive fixed point theory is presented, that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, best approximation theory, and convex feasibility. This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space
The book is suitable for graduate students and researchers in pure and applied mathematics, engineering and economics.” (Sergiu Aizicovici, Zentralblatt MATH, Vol. … The high level of the presentation, the careful and detailed discussion of many applications and algorithms, and last, but not least, the inclusion of more than four hundred exercises, make the book accessible and of great value to students, practitioners and researchers … .” (Simeon Reich, Mathematical Reviews, Issue 2012 h). From the reviews:“This book is devoted to a review of basic results and applications of convex analysis, monotone operator theory, and the theory of nonexpansive mappings in Hilbert spaces. … Each chapter concludes with an exercise section. 1218, 2011)“This timely, well-written,