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Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces

Part of MPS-SIAM Series on Optimization

Author: Michael Ulbrich, Technische Universität München

Date Published: July 2011
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Paperback
isbn: 9781611970685

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About the Authors

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, choosing a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments 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 • 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.
- Presents applications to PDE-constrained optimization, obstacle problems and flow control problems
- Includes new developments such as state-constrained problems and improved mesh independence results
- Contains many examples to illustrate theoretical results
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Product details
- Date Published: July 2011
- format: Paperback
- isbn: 9781611970685
- length: 320 pages
- dimensions: 244 x 177 x 15 mm
- weight: 0.58kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Notation
Preface
1. Introduction
2. Elements of finite-dimensional nonsmooth analysis
3. Newton methods for semismooth operator equations
4. Smoothing steps and regularity conditions
5. Variational inequalities and mixed problems
6. Mesh independence
7. Trust-region globalization
8. State-constrained and related problems
9. Several applications
10. Optimal control of incompressible Navier–Stokes flow
11. Optimal control of compressible Navier–Stokes flow
Appendix
Bibliography
Index.
Author
Michael Ulbrich, Technische Universität München
Michael Ulbrich is Professor and Chair of Mathematical Optimization in the Department of Mathematics at the Technische Universität München. His main research areas include numerical nonlinear optimization and its applications, optimal control with PDEs, and complementarity problems.