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Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Michael Ulbrich
出版SIAM, 2011-07-28
主題Mathematics / Linear & Nonlinear ProgrammingMathematics / GeneralMathematics / CalculusMathematics / Numerical AnalysisMathematics / Optimization
ISBN16119706879781611970685
URLhttp://books.google.com.hk/books?id=eNGlpOUhsyYC&hl=&source=gbs_api
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註釋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, choosing a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments 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 ? 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.