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
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.
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