Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces

Author : Michael Ulbrich
Publisher : SIAM
Page : 322 pages
File Size : 53,9 Mb
Release : 2011-01-01
Category : Constrained optimization
ISBN : 1611970695

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Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces by Michael Ulbrich Pdf

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 : Kazufumi Ito,Karl Kunisch
Publisher : SIAM
Page : 359 pages
File Size : 49,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 0898718619

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Lagrange Multiplier Approach to Variational Problems and Applications by Kazufumi Ito,Karl Kunisch Pdf

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,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 47,6 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9781402088391

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Optimization with PDE Constraints by Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich Pdf

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 : Alexey F. Izmailov,Mikhail V. Solodov
Publisher : Springer
Page : 587 pages
File Size : 50,5 Mb
Release : 2014-07-08
Category : Business & Economics
ISBN : 9783319042473

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Newton-Type Methods for Optimization and Variational Problems by Alexey F. Izmailov,Mikhail V. Solodov Pdf

This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Author : Thomas Carraro,Michael Geiger,Stefan Körkel,Rolf Rannacher
Publisher : Springer
Page : 422 pages
File Size : 46,5 Mb
Release : 2015-10-26
Category : Mathematics
ISBN : 9783319233215

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Multiple Shooting and Time Domain Decomposition Methods by Thomas Carraro,Michael Geiger,Stefan Körkel,Rolf Rannacher Pdf

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,Drew P. Kouri,Martin-D. Lacasse,Denis Ridzal
Publisher : Springer
Page : 434 pages
File Size : 50,7 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9781493986361

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Frontiers in PDE-Constrained Optimization by Harbir Antil,Drew P. Kouri,Martin-D. Lacasse,Denis Ridzal Pdf

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 : João M. F. Rodrigues,Pedro J. S. Cardoso,Jânio Monteiro,Roberto Lam,Valeria V. Krzhizhanovskaya,Michael H. Lees,Jack J. Dongarra,Peter M.A. Sloot
Publisher : Springer
Page : 744 pages
File Size : 50,7 Mb
Release : 2019-06-07
Category : Computers
ISBN : 9783030227449

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Computational Science – ICCS 2019 by João M. F. Rodrigues,Pedro J. S. Cardoso,Jânio Monteiro,Roberto Lam,Valeria V. Krzhizhanovskaya,Michael H. Lees,Jack J. Dongarra,Peter M.A. Sloot Pdf

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.

Author : Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Publisher : Springer
Page : 275 pages
File Size : 43,5 Mb
Release : 2019-01-26
Category : Science
ISBN : 9783030019594

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Numerical Methods for Optimal Control Problems by Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney Pdf

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Author : Achim Ilchmann,Timo Reis
Publisher : Springer
Page : 343 pages
File Size : 44,8 Mb
Release : 2014-12-04
Category : Mathematics
ISBN : 9783319110509

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Surveys in Differential-Algebraic Equations II by Achim Ilchmann,Timo Reis Pdf

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Observers for DAEs - DAEs in chemical processes - Optimal control of DAEs - DAEs from a functional-analytic viewpoint - Algebraic methods for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Author : Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat
Publisher : Walter de Gruyter GmbH & Co KG
Page : 474 pages
File Size : 46,9 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9783110695984

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Optimization and Control for Partial Differential Equations by Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat Pdf

This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Author : Juan Carlos De los Reyes
Publisher : Springer
Page : 123 pages
File Size : 55,5 Mb
Release : 2015-02-06
Category : Mathematics
ISBN : 9783319133959

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Numerical PDE-Constrained Optimization by Juan Carlos De los Reyes Pdf

This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Author : Matthias Gerdts
Publisher : Walter de Gruyter GmbH & Co KG
Page : 484 pages
File Size : 54,5 Mb
Release : 2023-11-06
Category : Technology & Engineering
ISBN : 9783110797893

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Optimal Control of ODEs and DAEs by Matthias Gerdts Pdf

Author : Amir Beck
Publisher : SIAM
Page : 487 pages
File Size : 45,9 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781611974997

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First-Order Methods in Optimization by Amir Beck Pdf

The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.

Author : Alfio Borzì
Publisher : CRC Press
Page : 267 pages
File Size : 48,7 Mb
Release : 2023-05-26
Category : Mathematics
ISBN : 9781000882469

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The Sequential Quadratic Hamiltonian Method by Alfio Borzì Pdf

The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP). The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Features Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems.

Author : Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli
Publisher : Birkhäuser
Page : 347 pages
File Size : 42,9 Mb
Release : 2018-02-13
Category : Mathematics
ISBN : 9783319708249

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New Trends in Parameter Identification for Mathematical Models by Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli Pdf

The Proceedings volume contains 16 contributions to the IMPA conference “New Trends in Parameter Identification for Mathematical Models”, Rio de Janeiro, Oct 30 – Nov 3, 2017, integrating the “Chemnitz Symposium on Inverse Problems on Tour”. This conference is part of the “Thematic Program on Parameter Identification in Mathematical Models” organized at IMPA in October and November 2017. One goal is to foster the scientific collaboration between mathematicians and engineers from the Brazialian, European and Asian communities. Main topics are iterative and variational regularization methods in Hilbert and Banach spaces for the stable approximate solution of ill-posed inverse problems, novel methods for parameter identification in partial differential equations, problems of tomography , solution of coupled conduction-radiation problems at high temperatures, and the statistical solution of inverse problems with applications in physics.