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

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by Michael Ulbrich


2011 / xiv + 308 / Softcover / ISBN: 978-1-611970-68-5 / List Price $109.00 / Member Price $76.30 / Order Code MO11

Keywords: semismooth Newton methods, PDE constrained optimization, variational inequality, complementarity, 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, 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. 

This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization, and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities. It is also suitable as a text for an advanced graduate-level course in the aforementioned topics or applied functional analysis.

About the Author
Michael Ulbrich is Professor and Chair of Mathematical Optimization in the Department of Mathematics at the Technische UniversitŠt MŸnchen. His main research interests include numerical nonlinear optimization and its applications, optimal control with PDEs, and complementarity problems.

ISBN: 9781611970685

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