Analysis And Optimization Of Differential Systems
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Optimization Of Elliptic Systems
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Author : Pekka Neittaanmaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
Optimization Of Elliptic Systems written by Pekka Neittaanmaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-08 with Mathematics categories.
The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.
Analysis And Optimization Of Differential Systems
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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-30
Analysis And Optimization Of Differential Systems written by Viorel Barbu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-30 with Mathematics categories.
Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations; Control theory of Partial Differential Equations (PDE's); Optimization methods in PDE's with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems. These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering. This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.
Optimization And Control For Partial Differential Equations
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Author : Roland Herzog
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-07
Optimization And Control For Partial Differential Equations written by Roland Herzog and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-07 with Mathematics categories.
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.
Real Time Pde Constrained Optimization
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Author : Lorenz T. Biegler
language : en
Publisher: SIAM
Release Date : 2007-01-01
Real Time Pde Constrained Optimization written by Lorenz T. Biegler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
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.
Optimal Control Of Partial Differential Equations
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Author : Andrea Manzoni
language : en
Publisher:
Release Date : 2021
Optimal Control Of Partial Differential Equations written by Andrea Manzoni and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a "hands-on" treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Large Scale Pde Constrained Optimization
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Author : Lorenz T. Biegler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Large Scale Pde Constrained Optimization written by Lorenz T. Biegler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Nonsmooth Analysis And Control Theory
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Author : Francis H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-10
Nonsmooth Analysis And Control Theory written by Francis H. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-10 with Mathematics categories.
In the last decades the subject of nonsmooth analysis has grown rapidly due to the recognition that nondifferentiable phenomena are more widespread, and play a more important role, than had been thought. In recent years, it has come to play a role in functional analysis, optimization, optimal design, mechanics and plasticity, differential equations, control theory, and, increasingly, in analysis. This volume presents the essentials of the subject clearly and succinctly, together with some of its applications and a generous supply of interesting exercises. The book begins with an introductory chapter which gives the reader a sampling of what is to come while indicating at an early stage why the subject is of interest. The next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject leading to an efficient, natural, yet powerful body of theory. The last chapter, as its name implies, is a self-contained introduction to thetheory of control of ordinary differential equations. End-of-chapter problems also offer scope for deeper understanding. The authors have incorporated in the text a number of new results which clarify the relationships between the different schools of thought in the subject. Their goal is to make nonsmooth analysis accessible to a wider audience. In this spirit, the book is written so as to be used by anyone who has taken a course in functional analysis.
Variational Methods In Shape Optimization Problems
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Author : Dorin Bucur
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-13
Variational Methods In Shape Optimization Problems written by Dorin Bucur and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-13 with Mathematics categories.
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Optimization With Pde Constraints
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Author : Michael Hinze
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-16
Optimization With Pde Constraints written by Michael Hinze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-16 with Mathematics categories.
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.
Analysis And Optimization Of Differential Systems
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Author : Viorel Barbu
language : en
Publisher: Springer
Release Date : 2013-03-06
Analysis And Optimization Of Differential Systems written by Viorel Barbu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-06 with Mathematics categories.
Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations; Control theory of Partial Differential Equations (PDE's); Optimization methods in PDE's with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems. These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering. This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.