Convex analysis and monotone operator theory in Hilbert spaces

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. Tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness.Accessible to a broad audience Coverage of many applications of interest to practitioners in infinite-dimensional spaces.More than 400 exercises are distributed throughout the book INDICE: 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.

• ISBN: 978-1-4419-9466-0
• Editorial: Springer New York
• Encuadernacion: Cartoné
• Páginas: 464
• Fecha Publicación: 29/04/2011
• Nº Volúmenes: 1
• Idioma: Inglés