Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces PDF Download
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| Author | : Michael Ulbrich |
| Publisher | : SIAM |
| Total Pages | : 322 |
| Release | : 2011-01-01 |
| Genre | : Constrained optimization |
| ISBN | : 9781611970692 |
Download Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book 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.
| Author | : Michael Ulbrich |
| Publisher | : SIAM |
| Total Pages | : 315 |
| Release | : 2011-07-28 |
| Genre | : Mathematics |
| ISBN | : 1611970687 |
Download Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book 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.
| Author | : Michael Ulbrich |
| Publisher | : |
| Total Pages | : 213 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
Download Nonsmooth Newton-like Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book in PDF, ePub and Kindle
| Author | : Kazufumi Ito |
| Publisher | : SIAM |
| Total Pages | : 359 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898718614 |
Download Lagrange Multiplier Approach to Variational Problems and Applications Book 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.
| Author | : Michael Hinze |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 279 |
| Release | : 2008-10-16 |
| Genre | : Mathematics |
| ISBN | : 1402088396 |
Download Optimization with PDE Constraints Book 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.
| Author | : David Gao |
| Publisher | : Springer |
| Total Pages | : 522 |
| Release | : 2014-11-11 |
| Genre | : Mathematics |
| ISBN | : 3319083775 |
Download Advances in Global Optimization Book in PDF, ePub and Kindle
This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.
| Author | : Thomas Carraro |
| Publisher | : Springer |
| Total Pages | : 424 |
| Release | : 2015-10-26 |
| Genre | : Mathematics |
| ISBN | : 3319233211 |
Download Multiple Shooting and Time Domain Decomposition Methods Book in PDF, ePub and Kindle
This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms. The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics. This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.
| Author | : Harbir Antil |
| Publisher | : Springer |
| Total Pages | : 434 |
| Release | : 2018-10-12 |
| Genre | : Mathematics |
| ISBN | : 1493986368 |
Download Frontiers in PDE-Constrained Optimization Book in PDF, ePub and Kindle
This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs). As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.
| Author | : Daniela Tonon |
| Publisher | : Springer |
| Total Pages | : 399 |
| Release | : 2017-09-01 |
| Genre | : Mathematics |
| ISBN | : 3319607715 |
Download Optimal Control: Novel Directions and Applications Book in PDF, ePub and Kindle
Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.
| Author | : João M. F. Rodrigues |
| Publisher | : Springer |
| Total Pages | : 744 |
| Release | : 2019-06-07 |
| Genre | : Computers |
| ISBN | : 3030227448 |
Download Computational Science – ICCS 2019 Book in PDF, ePub and Kindle
The five-volume set LNCS 11536, 11537, 11538, 11539 and 11540 constitutes the proceedings of the 19th International Conference on Computational Science, ICCS 2019, held in Faro, Portugal, in June 2019. The total of 65 full papers and 168 workshop papers presented in this book set were carefully reviewed and selected from 573 submissions (228 submissions to the main track and 345 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track; Track of Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Track of Agent-Based Simulations, Adaptive Algorithms and Solvers; Track of Applications of Matrix Methods in Artificial Intelligence and Machine Learning; Track of Architecture, Languages, Compilation and Hardware Support for Emerging and Heterogeneous Systems Part III: Track of Biomedical and Bioinformatics Challenges for Computer Science; Track of Classifier Learning from Difficult Data; Track of Computational Finance and Business Intelligence; Track of Computational Optimization, Modelling and Simulation; Track of Computational Science in IoT and Smart Systems Part IV: Track of Data-Driven Computational Sciences; Track of Machine Learning and Data Assimilation for Dynamical Systems; Track of Marine Computing in the Interconnected World for the Benefit of the Society; Track of Multiscale Modelling and Simulation; Track of Simulations of Flow and Transport: Modeling, Algorithms and Computation Part V: Track of Smart Systems: Computer Vision, Sensor Networks and Machine Learning; Track of Solving Problems with Uncertainties; Track of Teaching Computational Science; Poster Track ICCS 2019 Chapter “Comparing Domain-decomposition Methods for the Parallelization of Distributed Land Surface Models” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
