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.
Numerical PDE-Constrained Optimization
Numerical PDE-Constrained Optimization - 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 Numerical PDE-Constrained Optimization write by Juan Carlos De los Reyes. This book was released on 2015-02-06. Numerical PDE-Constrained Optimization available in PDF, EPUB and Kindle. 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.
Frontiers in PDE-Constrained Optimization
Frontiers in PDE-Constrained Optimization - 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 Frontiers in PDE-Constrained Optimization write by Harbir Antil. This book was released on 2018-10-12. Frontiers in PDE-Constrained Optimization available 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.
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 Ronald Hoppe. This book was released on 2014-09-11. Optimization with PDE Constraints available in PDF, EPUB and Kindle. 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).
Large-Scale PDE-Constrained Optimization
Large-Scale PDE-Constrained Optimization - 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 Large-Scale PDE-Constrained Optimization write by Lorenz T. Biegler. This book was released on 2012-12-06. Large-Scale PDE-Constrained Optimization available in PDF, EPUB and Kindle. 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.
