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

丛 书 名：MPS-SIAM Series on Optimization

作     者：Michael Ulbrich 

I S B N：(纸本) 9781611970685 

出 版 社：SIAM-Society for Industrial and Applied Mathematics 

出 版 年：2011年

主 题 词：constrained optimizat inequalities variational newton methods semismooth 

馆 藏 号：201769314...

摘      要：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 *** 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, including1) optimal control of nonlinear elliptic differential equations,2) obstacle problems,3) flow control of instationary Navier–Stokes *** addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative *** 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.