Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces (MPS-SIAM Series on Optimization)

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9781611970685: Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces (MPS-SIAM Series on Optimization)

Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications.

Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including optimal control of semilinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids.

In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.

Audience: This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization, and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities. It is also suitable as a text for an advanced graduate-level course in the aforementioned topics or applied functional analysis.

Contents: Notation; Preface; Chapter One: Introduction; Chapter Two: Elements of Finite-Dimensional Nonsmooth Analysis; Chapter Three: Newton Methods for Semismooth Operator Equations; Chapter Four: Smoothing Steps and Regularity Conditions; Chapter Five: Variational Inequalities and Mixed Problems; Chapter Six: Mesh Independence; Chapter Seven: Trust-Region Globalization; Chapter Eight: State-Constrained and Related Problems; Chapter Nine: Several Applications; Chapter Ten: Optimal Control of Incompressible Navier-Stokes Flow; Chapter Eleven: Optimal Control of Compressible Navier-Stokes Flow; Appendix; Bibliography; Index.

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Book Description:

A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.

About the Author:

Michael Ulbrich is Professor and Chair of Mathematical Optimization in the Department of Mathematics at the Technische Universitat Munchen. His main research areas include numerical nonlinear optimization and its applications, optimal control with PDEs, and complementarity problems.

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Book Description Society for Industrial Applied Mathematics,U.S., United States, 2011. Paperback. Book Condition: New. New.. 254 x 178 mm. Language: English . Brand New Book. Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including optimal control of semilinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods. Bookseller Inventory # AAN9781611970685

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Book Description Society for Industrial Applied Mathematics,U.S., United States, 2011. Paperback. Book Condition: New. New.. 254 x 178 mm. Language: English . Brand New Book. Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including optimal control of semilinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods. Bookseller Inventory # AAN9781611970685

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