Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Published on 28. July 2011
Book
Paperback/Softback
320 pages
978-1-61197-068-5 (ISBN)
Description
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.
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.
More details
Person
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.
Content
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.