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

Michael Ulbrich

ISBN 10: 1611970687 / ISBN 13: 9781611970685

Published by Society for Industrial and Applied Mathematics,U.S., US, 2011

About this Item

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.

Seller Inventory # LU-9781611970685

Bibliographic Details

• Title: Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
• Publisher: Society for Industrial and Applied Mathematics,U.S., US
• Publication Date: 2011
• Language: English
• ISBN 10: 1611970687
• ISBN 13: 9781611970685
• Binding: Paperback
• Condition: New
• Weight: 580 grams

About this title

Synopsis

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.

About the Author

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.