Semismooth Newton methods for variational inequalities and constrained optimization problems in function spaces / Michael Ulbrich.

Format:

Book

Author/Creator:

Ulbrich, Michael.

Contributor:

Society for Industrial and Applied Mathematics.

Series:

MOS-SIAM series on optimization.

MOS-SIAM series on optimization

Language:

English

Subjects (All):

Function spaces.

Constrained optimization.

Variational inequalities (Mathematics).

Newton-Raphson method.

Physical Description:

1 electronic text (xiv, 308 p.) : digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2011.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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 nonlinear 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.

Contents:

Notation

Preface

Chapter 1. Introduction

Chapter 2. Elements of finite-dimensional nonsmooth analysis

Chapter 3. Newton methods for semismooth operator equations

Chapter 4. Smoothing steps and regularity conditions

Chapter 5. Variational inequalities and mixed problems

Chapter 6. Mesh independence

Chapter 7. Trust-region globalization

Chapter 8. State-constrained and related problems

Chapter 9. Several applications

Chapter 10. Optimal control of incompressible Navier-Stokes flow

Chapter 11. Optimal control of compressible Navier-Stokes flow

Appendix

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 05/31/2011.

ISBN:

1-61197-069-5

Publisher Number:

MO11 SIAM