Bauschke H.H., Combettes P.L. Convex analysis and monotone operator theory in Hilbert spaces

Springer, 2011. — 486 p.
This self-contained book offers a modern unifying presentation of three basic areas of nonlinear analysis, namely convex analysis, monotone operator theory, and the fixed point theory of nonexpansive mappings. This turns out to be a judicious choice. Showing the rich connections
and interplay between these topics gives a strong coherence to the book. Moreover, these particular topics are at the core of modern optimization and its applications.
Choosing to work in Hilbert spaces offers a wide range of applications, while keeping the mathematics accessible to a large audience. Each topic is
developed in a self-contained fashion, and the presentation often draws on recent advances.
The organization of the book makes it accessible to a large audience. Each chapter is illustrated by several exercises, which makes the monograph an excellent textbook. In addition, it offers deep insights into algorithmic aspects of optimization, especially splitting algorithms, which are important in theory and applications.