Optimization with PDE Constraints

This book PDF is perfect for those who love Mathematics genre, written by Michael Hinze and published by Springer Science & Business Media which was released on 16 October 2008 with total hardcover pages 279. You could read this book directly on your devices with pdf, epub and kindle format, check detail and related Optimization with PDE Constraints books below.

Optimization with PDE Constraints
Optimization with PDE Constraints
Author : Michael Hinze
File Size : 43,7 Mb
Publisher : Springer Science & Business Media
Language : English
Release Date : 16 October 2008
ISBN : 9781402088391
Pages : 279 pages
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Optimization with PDE Constraints by Michael Hinze Book PDF Summary

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.

Optimization with PDE Constraints

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

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

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Constrained Optimization and Optimal Control for Partial Differential Equations

Constrained Optimization and Optimal Control for Partial Differential Equations by Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field.

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Numerical PDE Constrained Optimization

Numerical PDE Constrained Optimization by Juan Carlos De los Reyes

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

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Optimization with PDE Constraints

Optimization with PDE Constraints by Ronald Hoppe

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

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Frontiers in PDE Constrained Optimization

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

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

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Real time PDE constrained Optimization

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

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

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Large Scale PDE Constrained Optimization

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

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,

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Control and Optimization with PDE Constraints

Control and Optimization with PDE Constraints by Kristian Bredies,Christian Clason,Karl Kunisch,Gregory von Winckel

Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full

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