Semismooth Newton methods for variationa
โ Ulbrich M.
๐ Library
๐
2011
๐ English
โฆ LIBER โฆ
๐
Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
โ Scribed by Michael Ulbrich
- Publisher
- Society for Industrial & Applied Mathematics
- Year
- 2011
- Tongue
- English
- Leaves
- 315
- Series
- MPS-SIAM Series on Optimization
- Category
- Library
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โฆ 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, 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 semilinear 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.
Audience: 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.
Contents: Notation; Preface; Chapter One: Introduction; Chapter Two: Elements of Finite-Dimensional Nonsmooth Analysis; Chapter Three: Newton Methods for Semismooth Operator Equations; Chapter Four: Smoothing Steps and Regularity Conditions; Chapter Five: Variational Inequalities and Mixed Problems; Chapter Six: Mesh Independence; Chapter Seven: Trust-Region Globalization; Chapter Eight: State-Constrained and Related Problems; Chapter Nine: Several Applications; Chapter Ten: Optimal Control of Incompressible Navier-Stokes Flow; Chapter Eleven: Optimal Control of Compressible Navier-Stokes Flow; Appendix; Bibliography; Index
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