The Resource Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels
Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels
 Summary
 "Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, secondorder sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the KarushKuhnTucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book selfcontained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly selfcontained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDEconstrained optimization."Publisher's description
 Language

 eng
 ger
 eng
 Extent
 xv, 399 p.
 Contents

 Introduction and examples
 Linearquadratic elliptic control problems
 Linearquadratic parabolic control problems
 Optimal control of semilinear elliptic equations
 Optimal control of semilinear parabolic equations
 Optimization problems in Banach spaces
 Supplementary results on partial differential equations
 Isbn
 9780821849040
 Label
 Optimal control of partial differential equations : theory, methods, and applications
 Title
 Optimal control of partial differential equations
 Title remainder
 theory, methods, and applications
 Statement of responsibility
 Fredi Tröltzsch ; translated by Jürgen Sprekels
 Language

 eng
 ger
 eng
 Summary
 "Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, secondorder sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the KarushKuhnTucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book selfcontained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly selfcontained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDEconstrained optimization."Publisher's description
 Cataloging source
 DLC
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA402.3
 LC item number
 .T71913 2010
 Literary form
 non fiction
 Nature of contents
 bibliography
 Series statement
 Graduate studies in mathematics :
 Series volume
 v. 112
 Label
 Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels
 Bibliography note
 Includes bibliographical references and index
 Contents
 Introduction and examples  Linearquadratic elliptic control problems  Linearquadratic parabolic control problems  Optimal control of semilinear elliptic equations  Optimal control of semilinear parabolic equations  Optimization problems in Banach spaces  Supplementary results on partial differential equations
 http://library.link/vocab/cover_art
 https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9780821849040&userID=ebscotest&password=ebscotest
 Dimensions
 26 cm.
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b3368833'}
 Extent
 xv, 399 p.
 Isbn
 9780821849040
 Isbn Type
 (alk. paper)
 Lccn
 2009037756
 Other physical details
 ill.
 System control number
 (OCoLC)441945348
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