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Full 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.
Contents
* Notation* Preface* Chapter OneFinite-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.
