[PDF] Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces (MPS-SIAM Series on Optimization)

ISBN: 1611970687

Category: Tutorial


Posted on 2017-10-30, by luongquocchinh.

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Author: Michael Ulbrich | Category: Mathematics | Language: English | Page: 322 | ISBN: 1611970687 | ISBN13: 9781611970685 |

Description: 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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