Bookstore

This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. 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. 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.

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Background.- Hilbert Spaces.- Convex sets.- Convexity and Nonexpansiveness.- Fej er Monotonicity and Fixed Point Iterations.- Convex Cones and Generalized Interiors.- Support Functions and Polar Sets.- Convex Functions.- Lower Semicontinuous Convex Functions.- Convex Functions: Variants.- Convex Variational Problems.- Infimal Convolution.- Conjugation.- Further Conjugation Results.- Fenchel-Rockafellar Duality.- Subdifferentiability.- Differentiability of Convex Functions.- Further Differentiability Results.- Duality in Convex Optimization.- Monotone Operators.- Finer Properties of Monotone Operators.- Stronger Notions of Monotonicity.- Resolvents of Monotone Operators.- Sums of Monotone Operators.-Zeros of Sums of Monotone Operators.- Fermat's Rule in Convex Optimization.- Proximal Minimization Projection Operators.- Best Approximation Algorithms.- Bibliographical Pointers.- Symbols and Notation.- References.