Librería Portfolio

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



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.