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

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