finelybook
Convex Analysis and Monotone Operator Theory in Hilbert Spaces (CMS Books in Mathematics)
by 作者: Heinz H. Bauschke and Patrick L. Combettes
Publisher Finelybook 出版社: ; 2nd ed. 2017 edition (March 8,2017)
Language 语言: English
pages 页数: 638 pages
ISBN-10 书号: 3319483102
ISBN-13 书号: 9783319483108
Book Description
This reference text,now in its second edition,offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis,monotone operator theory,and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach,the theory is developed from the ground up,with the rich connections and interactions between the areas as the central focus,and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces.The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises,this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering,data science,machine learning,physics,decision sciences,economics,and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition,containing over 140 pages of new material,over 270 new results,and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions,in addition to several new sections distributed throughout the original chapters. Many existing results have been improved,and the list of references has been updated.
Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia,Canada.
Patrick L. Combettes,IEEE Fellow,was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Table of contents:
Front Matter....Pages i-xix
Background....Pages 1-26
Hilbert Spaces....Pages 27-47
Convex Sets....Pages 49-68
Convexity and Notions of Nonexpansiveness....Pages 69-89
Fejér Monotonicity and Fixed Point Iterations....Pages 91-109
Convex Cones and Generalized Interiors....Pages 111-132
Support Functions and Polar Sets....Pages 133-138
Convex Functions....Pages 139-156
Lower Semicontinuous Convex Functions....Pages 157-176
Convex Functions: Variants....Pages 177-187
Convex Minimization Problems....Pages 189-201
Infimal Convolution....Pages 203-217
Conjugation....Pages 219-236
Further Conjugation Results....Pages 237-246
Fenchel–Rockafellar Duality....Pages 247-262
Subdifferentiability of Convex Functions....Pages 263-287
Differentiability of Convex Functions....Pages 289-312
Further Differentiability Results....Pages 313-327
Duality in Convex Optimization....Pages 329-347
Monotone Operators....Pages 349-368
Finer Properties of Monotone Operators....Pages 369-381
Stronger Notions of Monotonicity....Pages 383-392
Resolvents of Monotone Operators....Pages 393-412
Proximity Operators....Pages 413-446
Sums of Monotone Operators....Pages 447-463
Zeros of Sums of Monotone Operators....Pages 465-495
Fermat’s Rule in Convex Optimization....Pages 497-514
Proximal Minimization....Pages 515-534
Projection Operators....Pages 535-560
Best Approximation Algorithms....Pages 561-575
Back Matter....Pages 577-619
