Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces write by Michael Ulbrich. This book was released on 2011-01-01. Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces available in PDF, EPUB and Kindle. 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 nonlinear 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.
Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces write by Michael Ulbrich. This book was released on 2011-07-28. Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces available in PDF, EPUB and Kindle. A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. 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.
Nonsmooth Newton-like Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Nonsmooth Newton-like Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonsmooth Newton-like Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces write by Michael Ulbrich. This book was released on 2002. Nonsmooth Newton-like Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces available in PDF, EPUB and Kindle.
Lagrange Multiplier Approach to Variational Problems and Applications
Lagrange Multiplier Approach to Variational Problems and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lagrange Multiplier Approach to Variational Problems and Applications write by Kazufumi Ito. This book was released on 2008-01-01. Lagrange Multiplier Approach to Variational Problems and Applications available in PDF, EPUB and Kindle. Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.
Optimization with PDE Constraints
Optimization with PDE Constraints - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimization with PDE Constraints write by Michael Hinze. This book was released on 2008-10-16. Optimization with PDE Constraints available in PDF, EPUB and Kindle. Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
