Trends In Pde Constrained Optimization

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Trends in PDE Constrained Optimization

Günter Leugering,Peter Benner,Sebastian Engell,Andreas Griewank,Helmut Harbrecht,Michael Hinze,Rolf Rannacher,Stefan Ulbrich
Trends in PDE Constrained Optimization Book PDF

Author : Günter Leugering,Peter Benner,Sebastian Engell,Andreas Griewank,Helmut Harbrecht,Michael Hinze,Rolf Rannacher,Stefan Ulbrich
Publisher : Springer
Page : 539 pages
File Size : 46,6 Mb
Release : 2014-12-22
Category : Mathematics
ISBN : 9783319050836

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Trends in PDE Constrained Optimization by Günter Leugering,Peter Benner,Sebastian Engell,Andreas Griewank,Helmut Harbrecht,Michael Hinze,Rolf Rannacher,Stefan Ulbrich Pdf

Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

Real-time PDE-constrained Optimization

Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bart van Bloemen Waanders
Real time PDE constrained Optimization Book PDF

Author : Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bart van Bloemen Waanders
Publisher : SIAM
Page : 335 pages
File Size : 43,6 Mb
Release : 2007-01-01
Category : Differential equations, Partial
ISBN : 0898718937

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Real-time PDE-constrained Optimization by Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bart van Bloemen Waanders Pdf

Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.

Frontiers in PDE-Constrained Optimization

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

Author : Harbir Antil,Drew P. Kouri,Martin-D. Lacasse,Denis Ridzal
Publisher : Springer
Page : 434 pages
File Size : 51,7 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.

Large-Scale PDE-Constrained Optimization

Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders
Large Scale PDE Constrained Optimization Book PDF

Author : Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642555084

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Large-Scale PDE-Constrained Optimization by Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders Pdf

Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Large-Scale PDE-Constrained Optimization in Applications

Subhendu Bikash Hazra
Large Scale PDE Constrained Optimization in Applications Book PDF

Author : Subhendu Bikash Hazra
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 45,8 Mb
Release : 2009-12-16
Category : Mathematics
ISBN : 9783642015021

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Large-Scale PDE-Constrained Optimization in Applications by Subhendu Bikash Hazra Pdf

With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.

Optimization with PDE Constraints

Ronald Hoppe
Optimization with PDE Constraints Book PDF

Author : Ronald Hoppe
Publisher : Springer
Page : 402 pages
File Size : 42,7 Mb
Release : 2014-09-11
Category : Computers
ISBN : 9783319080253

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Optimization with PDE Constraints by Ronald Hoppe Pdf

This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).

Optimization with PDE Constraints

Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Optimization with PDE Constraints Book PDF

Author : Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer
Page : 0 pages
File Size : 48,7 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9048180031

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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.

New Trends in Shape Optimization

Aldo Pratelli,Günter Leugering
New Trends in Shape Optimization Book PDF

Author : Aldo Pratelli,Günter Leugering
Publisher : Birkhäuser
Page : 314 pages
File Size : 44,9 Mb
Release : 2015-12-01
Category : Mathematics
ISBN : 9783319175638

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New Trends in Shape Optimization by Aldo Pratelli,Günter Leugering Pdf

This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

Numerical PDE-Constrained Optimization

Juan Carlos De los Reyes
Numerical PDE Constrained Optimization Book PDF

Author : Juan Carlos De los Reyes
Publisher : Springer
Page : 123 pages
File Size : 46,9 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.

Numerical PDE Constrained Optimization

Matthias Heinkenschloss,Lu's Merca Fernandes,Luis Nunes Vicente
Numerical PDE Constrained Optimization Book PDF

Author : Matthias Heinkenschloss,Lu's Merca Fernandes,Luis Nunes Vicente
Publisher : Springer Verlag
Page : 300 pages
File Size : 50,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3540773282

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Numerical PDE Constrained Optimization by Matthias Heinkenschloss,Lu's Merca Fernandes,Luis Nunes Vicente Pdf

The efficient numerical solution of PDE constrained optimization problems plays an important role in many engineering and science applications. The development of robust and efficient numerical algorithms requires the integration of tools from several mathematical subdisciplines, often only described individually in books or journal articles. The goal of this book is to provide readers with a brief introduction to this active research area as well as with an overview of the state-of-the-art in the important topics of adaptive discretizations of PDE optimization problems, handling of control and state constraints, domain decomposition and homogenization of PDEs on networks, and reduced order modeling.

Realization and Model Reduction of Dynamical Systems

Christopher Beattie,Peter Benner,Mark Embree,Serkan Gugercin,Sanda Lefteriu
Realization and Model Reduction of Dynamical Systems Book PDF

Author : Christopher Beattie,Peter Benner,Mark Embree,Serkan Gugercin,Sanda Lefteriu
Publisher : Springer Nature
Page : 462 pages
File Size : 55,8 Mb
Release : 2022-06-09
Category : Science
ISBN : 9783030951573

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Realization and Model Reduction of Dynamical Systems by Christopher Beattie,Peter Benner,Mark Embree,Serkan Gugercin,Sanda Lefteriu Pdf

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.

Optimization and Control for Partial Differential Equations

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

Author : Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat
Publisher : Walter de Gruyter GmbH & Co KG
Page : 386 pages
File Size : 48,8 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9783110696004

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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.

Numerical PDE Constrained Optimization

Matthias Heinkenschloss,Luis Nunes Vicente,Luis Merca Fernandes
Numerical PDE Constrained Optimization Book PDF

Author : Matthias Heinkenschloss,Luis Nunes Vicente,Luis Merca Fernandes
Publisher : Springer
Page : 128 pages
File Size : 41,5 Mb
Release : 2010-11-16
Category : Mathematics
ISBN : 3540870016

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Numerical PDE Constrained Optimization by Matthias Heinkenschloss,Luis Nunes Vicente,Luis Merca Fernandes Pdf

The efficient numerical solution of PDE constrained optimization problems plays an important role in many engineering and science applications. The development of robust and efficient numerical algorithms requires the integration of tools from several mathematical subdisciplines, often only described individually in books or journal articles. The goal of this book is to provide readers with a brief introduction to this active research area as well as with an overview of the state-of-the-art in the important topics of adaptive discretizations of PDE optimization problems, handling of control and state constraints, domain decomposition and homogenization of PDEs on networks, and reduced order modeling.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 Book PDF

Author : Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
Publisher : Springer Nature
Page : 658 pages
File Size : 50,7 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9783030396473

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 by Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab Pdf

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Domain Decomposition Methods in Science and Engineering XXIV

Petter E. Bjørstad,Susanne C. Brenner,Lawrence Halpern,Hyea Hyun Kim,Ralf Kornhuber,Talal Rahman,Olof B. Widlund
Domain Decomposition Methods in Science and Engineering XXIV Book PDF

Author : Petter E. Bjørstad,Susanne C. Brenner,Lawrence Halpern,Hyea Hyun Kim,Ralf Kornhuber,Talal Rahman,Olof B. Widlund
Publisher : Springer
Page : 570 pages
File Size : 53,9 Mb
Release : 2019-01-05
Category : Mathematics
ISBN : 9783319938738

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Domain Decomposition Methods in Science and Engineering XXIV by Petter E. Bjørstad,Susanne C. Brenner,Lawrence Halpern,Hyea Hyun Kim,Ralf Kornhuber,Talal Rahman,Olof B. Widlund Pdf

These are the proceedings of the 24th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Svalbard, Norway in February 2017. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2017.