Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces
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Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Author | : Michael Ulbrich |
Publisher | : SIAM |
Total Pages | : 322 |
Release | : 2011-01-01 |
Genre | : Constrained optimization |
ISBN | : 9781611970692 |
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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 nonlinear 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.
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