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

A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field.

Michael Ulbrich (Author)

9781611970685

Paperback / softback, published 30 July 2011

322 pages
25.1 x 17.7 x 1.7 cm, 0.592 kg

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.

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.

Subject Areas: Miscellaneous items [WZ]