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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization: v. 40 (Applied Optimization) - Hardcover
Inhaltsangabe
1: Totally Convex Functions.- 1.1. Convex Functions and Bregman Distances.- 1.2. The Modulus of Total Convexity.- 1.3. Total Versus Locally Uniform Convexity.- 1.4. Particular Totally Convex Functions.- 2: Computation of Fixed Points.- 2.1. Totally Nonexpansive Operators.- 2.2. Totally Nonexpansive Families of Operators.- 2.3. Stochastic Convex Feasibility Problems.- 2.4. Applications in Particular Banach Spaces.- 3: Infinite Dimensional Optimization.- 3.1. A Proximal Point Method.- 3.2. Convergence of the Proximal Point Method.- 3.3. The Basics of a Duality Theory.- 3.4. An Augmented Lagrangian Method.- 3.5. Unconstrained Convex Minimization.
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The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, `total convexity', is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making our general approach possible we had to improve upon classical results like the Hölder-Minkowsky inequality of Lp. All the material is either new or very recent, and has never been organized in a book. Audience: This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc.
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TOTALLY CONVEX FUNCTIONS FOR FIXED POINTS COMPUTATION AND INFINITE DIMENSIONAL OPTIMIZATION
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Kluwer Academic Publishers, Dordrecht, 2000
ISBN 10: 079236287X
ISBN 13: 9780792362876
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, `total convexity', is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making our general approach possible we had to improve upon classical results like the Hölder-Minkowsky inequality of Lp. All the material is either new or very recent, and has never been organized in a book. Audience: This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc. 224 pp. Englisch. Bestandsnummer des Verkäufers 9780792362876
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, `total convexity', is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making our general approach possible we had to improve upon classical results like the Hölder-Minkowsky inequality of Lp. All the material is either new or very recent, and has never been organized in a book. Audience: This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc. Bestandsnummer des Verkäufers 9780792362876
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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
Verlag:
Springer Netherlands|Springer, Berlin, 2000
ISBN 10: 079236287X
ISBN 13: 9780792362876
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Zustand: New. The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many con. Bestandsnummer des Verkäufers 898699151
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