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Título : Optimal Control Models in Finance : A New Computational Approach Tipo de documento: documento electrónico Autores: Chen, Ping ; SpringerLink (Online service) ; Islam, Sardar M. N Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Applied Optimization, ISSN 1384-6485 num. 95 Número de páginas: XVIII, 201 p Il.: online resource ISBN/ISSN/DL: 978-0-387-23570-7 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical optimization Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: The determination of optimal financing and investment strategies (optimal capital structure or optimal mix of funds, optimal portfolio choice, etc.) for corporations and the economy are important for efficient allocation of resources in the economy. Optimal control methods have useful applications to these areas in finance - some optimization problems in finance include optimal control, involving a dynamic system with switching times in the form of bang-bang control. Optimal control models for corporate finance and the economy are presented in this book and the analytical and computational results of these models are also reported. Such computational approaches to the study of optimal corporate financing are not well known in the existing literature. This book develops a new computational method where switching times are considered as variables in the optimal dynamic financial model represented by a second order differential equation. A new computer program named CSTVA (Computer Program for the Switching Time Variables Algorithm), which can compute bang-bang optimal financial models with switching time, is also developed. Optimal financing implications of the model results in the form of optimal switching times for changes in financing policies and the optimal financial policies are analyzed Nota de contenido: Optimal Control Models in Finance -- The STV Approach to Financial Optimal Control Models -- A Financial Oscillator Model -- An Optimal Corporate Financing Model -- Further Computational Experiments and Results -- Conclusion En línea: http://dx.doi.org/10.1007/b101888 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35071 Optimal Control Models in Finance : A New Computational Approach [documento electrónico] / Chen, Ping ; SpringerLink (Online service) ; Islam, Sardar M. N . - Boston, MA : Springer US, 2005 . - XVIII, 201 p : online resource. - (Applied Optimization, ISSN 1384-6485; 95) .
ISBN : 978-0-387-23570-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical optimization Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: The determination of optimal financing and investment strategies (optimal capital structure or optimal mix of funds, optimal portfolio choice, etc.) for corporations and the economy are important for efficient allocation of resources in the economy. Optimal control methods have useful applications to these areas in finance - some optimization problems in finance include optimal control, involving a dynamic system with switching times in the form of bang-bang control. Optimal control models for corporate finance and the economy are presented in this book and the analytical and computational results of these models are also reported. Such computational approaches to the study of optimal corporate financing are not well known in the existing literature. This book develops a new computational method where switching times are considered as variables in the optimal dynamic financial model represented by a second order differential equation. A new computer program named CSTVA (Computer Program for the Switching Time Variables Algorithm), which can compute bang-bang optimal financial models with switching time, is also developed. Optimal financing implications of the model results in the form of optimal switching times for changes in financing policies and the optimal financial policies are analyzed Nota de contenido: Optimal Control Models in Finance -- The STV Approach to Financial Optimal Control Models -- A Financial Oscillator Model -- An Optimal Corporate Financing Model -- Further Computational Experiments and Results -- Conclusion En línea: http://dx.doi.org/10.1007/b101888 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35071 Ejemplares
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Título : Optimal Stopping and Free-Boundary Problems Tipo de documento: documento electrónico Autores: Peskir, Goran ; SpringerLink (Online service) ; Shiryaev, Albert Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2006 Colección: Lectures in Mathematics. ETH Zürich Número de páginas: XXII, 502 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7390-0 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Economics, Mathematical Calculus of variations Probabilities Probability Theory and Stochastic Processes Variations Optimal Control; Optimization Differential Equations Quantitative Finance Clasificación: 51 Matemáticas Resumen: The present monograph, based mainly on studies of the authors and their - authors, and also on lectures given by the authors in the past few years, has the following particular aims: To present basic results (with proofs) of optimal stopping theory in both discrete and continuous time using both martingale and Mar- vian approaches; To select a seriesof concrete problems ofgeneral interest from the t- ory of probability, mathematical statistics, and mathematical ?nance that can be reformulated as problems of optimal stopping of stochastic processes and solved by reduction to free-boundary problems of real analysis (Stefan problems). The table of contents found below gives a clearer idea of the material included in the monograph. Credits and historical comments are given at the end of each chapter or section. The bibliography contains a material for further reading. Acknowledgements.TheauthorsthankL.E.Dubins,S.E.Graversen,J.L.Ped- sen and L. A. Shepp for useful discussions. The authors are grateful to T. B. To- zovafortheexcellenteditorialworkonthemonograph.Financialsupportandh- pitality from ETH, Zur ¨ ich (Switzerland), MaPhySto (Denmark), MIMS (Man- ester) and Thiele Centre (Aarhus) are gratefully acknowledged. The authors are also grateful to INTAS and RFBR for the support provided under their grants. The grant NSh-1758.2003.1 is gratefully acknowledged. Large portions of the text were presented in the “School and Symposium on Optimal Stopping with App- cations” that was held in Manchester, England from 17th to 27th January 2006 Nota de contenido: Optimal stopping: General facts -- Stochastic processes: A brief review -- Optimal stopping and free-boundary problems -- Methods of solution -- Optimal stopping in stochastic analysis -- Optimal stopping in mathematical statistics -- Optimal stopping in mathematical finance -- Optimal stopping in financial engineering En línea: http://dx.doi.org/10.1007/978-3-7643-7390-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35004 Optimal Stopping and Free-Boundary Problems [documento electrónico] / Peskir, Goran ; SpringerLink (Online service) ; Shiryaev, Albert . - Basel : Birkhäuser Basel, 2006 . - XXII, 502 p : online resource. - (Lectures in Mathematics. ETH Zürich) .
ISBN : 978-3-7643-7390-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Economics, Mathematical Calculus of variations Probabilities Probability Theory and Stochastic Processes Variations Optimal Control; Optimization Differential Equations Quantitative Finance Clasificación: 51 Matemáticas Resumen: The present monograph, based mainly on studies of the authors and their - authors, and also on lectures given by the authors in the past few years, has the following particular aims: To present basic results (with proofs) of optimal stopping theory in both discrete and continuous time using both martingale and Mar- vian approaches; To select a seriesof concrete problems ofgeneral interest from the t- ory of probability, mathematical statistics, and mathematical ?nance that can be reformulated as problems of optimal stopping of stochastic processes and solved by reduction to free-boundary problems of real analysis (Stefan problems). The table of contents found below gives a clearer idea of the material included in the monograph. Credits and historical comments are given at the end of each chapter or section. The bibliography contains a material for further reading. Acknowledgements.TheauthorsthankL.E.Dubins,S.E.Graversen,J.L.Ped- sen and L. A. Shepp for useful discussions. The authors are grateful to T. B. To- zovafortheexcellenteditorialworkonthemonograph.Financialsupportandh- pitality from ETH, Zur ¨ ich (Switzerland), MaPhySto (Denmark), MIMS (Man- ester) and Thiele Centre (Aarhus) are gratefully acknowledged. The authors are also grateful to INTAS and RFBR for the support provided under their grants. The grant NSh-1758.2003.1 is gratefully acknowledged. Large portions of the text were presented in the “School and Symposium on Optimal Stopping with App- cations” that was held in Manchester, England from 17th to 27th January 2006 Nota de contenido: Optimal stopping: General facts -- Stochastic processes: A brief review -- Optimal stopping and free-boundary problems -- Methods of solution -- Optimal stopping in stochastic analysis -- Optimal stopping in mathematical statistics -- Optimal stopping in mathematical finance -- Optimal stopping in financial engineering En línea: http://dx.doi.org/10.1007/978-3-7643-7390-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35004 Ejemplares
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Título : Optimal Control Tipo de documento: documento electrónico Autores: Vinter, Richard ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Modern Birkhäuser Classics Número de páginas: XX, 500 p. 13 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8086-2 Idioma : Inglés (eng) Palabras clave: Mathematics System theory Calculus of variations Control engineering Systems Theory, Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton–Jacobi equation. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subject’s key concepts and foundations. Features and Topics: * a comprehensive overview is provided for specialists and nonspecialists * authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control * chapter coverage of dynamic programming and the regularity of minimizers * explains the necessary conditions for nonconvex problems This book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, and professionals in systems, control, optimization, and applied mathematics. ----- Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control.—Mathematical Reviews This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices. ... Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis). —Automatica The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition.—Applications of Mathematics Nota de contenido: Overview -- Measurable Multifunctions and Differential Inclusions -- Variational Principles -- Nonsmooth Analysis -- Subdifferential Calculus -- The Maximum Principle -- The Extended Euler–Lagrange and Hamilton Conditions -- Necessary Conditions for Free End-Time Problems -- The Maximum Principle for State Constrained Problems -- Necessary Conditions for Differential Inclusion Problems with State Constraints -- Regularity of Minimizers -- Dynamic Programming En línea: http://dx.doi.org/10.1007/978-0-8176-8086-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33567 Optimal Control [documento electrónico] / Vinter, Richard ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XX, 500 p. 13 illus : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-8086-2
Idioma : Inglés (eng)
Palabras clave: Mathematics System theory Calculus of variations Control engineering Systems Theory, Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton–Jacobi equation. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subject’s key concepts and foundations. Features and Topics: * a comprehensive overview is provided for specialists and nonspecialists * authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control * chapter coverage of dynamic programming and the regularity of minimizers * explains the necessary conditions for nonconvex problems This book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, and professionals in systems, control, optimization, and applied mathematics. ----- Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control.—Mathematical Reviews This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices. ... Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis). —Automatica The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition.—Applications of Mathematics Nota de contenido: Overview -- Measurable Multifunctions and Differential Inclusions -- Variational Principles -- Nonsmooth Analysis -- Subdifferential Calculus -- The Maximum Principle -- The Extended Euler–Lagrange and Hamilton Conditions -- Necessary Conditions for Free End-Time Problems -- The Maximum Principle for State Constrained Problems -- Necessary Conditions for Differential Inclusion Problems with State Constraints -- Regularity of Minimizers -- Dynamic Programming En línea: http://dx.doi.org/10.1007/978-0-8176-8086-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33567 Ejemplares
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Título : Optimal Control of Distributed Systems with Conjugation Conditions Tipo de documento: documento electrónico Autores: Sergienko, Ivan V ; SpringerLink (Online service) ; Deineka, Vasyl S ; Shor, Naum Z Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Nonconvex Optimization and Its Applications, ISSN 1571-568X num. 75 Número de páginas: XVI, 383 p Il.: online resource ISBN/ISSN/DL: 978-0-387-24256-9 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Mathematical optimization Calculus of variations Variations and Optimal Control; Optimization Differential Equations Clasificación: 51 Matemáticas Resumen: This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, pseudoparabolic, hyperbolic, and pseudohyperbolic equations and with elasticity theory equation systems that have nonsmooth solutions, including discontinuous solutions. With the basis of this methodology, the monograph shows a continuous dependence of states, namely, of solutions to the enumerated boundary-value and initial boundary-value problems (including discontinuous states) and a dependence of solution traces on distributed controls and controls at sectors of n-dimensional domain boundaries and at n–1-dimensional function-state discontinuity surfaces (i.e., at mean surfaces of thin inclusions in heterogeneous media). Such an aspect provides the existence of optimal controls for the mentioned systems with J.L. Lions’ quadratic cost functionals. Besides this, the authors consider some new systems, for instance, the ones described by the conditionally correct Neumann problems with unique states on convex sets, and such states admit first-order discontinuities. These systems are also described by quartic equations with conjugation conditions, by parabolic equations with constraints that contain first-order time state derivatives in the presence of concentrated heat capacity, and by elasticity theory equations. In a number of cases, when a set of feasible controls coincides with corresponding Hilbert spaces, the authors propose to use the computational algorithms for the finite-element method. Such algorithms have the increased order of the accuracy with which optimal controls are numerically found. Audience This book is intended for specialists in applied mathematics, scientific researchers, engineers, and postgraduate students interested in optimal control of heterogeneous distributed systems with states described by boundary-value and initial boundary-value problems Nota de contenido: Control of Systems Described by Elliptic-Type Partial-Differential Equations under Conjugation Conditions -- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation under Conjugation Conditions -- Control of a System Described by a One-Dimensional Quartic Equation under Conjugation Conditions -- Control of a System Described by a Two-Dimensional Quartic Equation under Conjugation Conditions -- Control of a System Described by a Parabolic Equation under Conjugation Conditions -- Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity -- Control of a System Described by a Pseudoparabolic Equation under Conjugation Conditions -- Control of a System Described by a Hyperbolic Equation under Conjugation Conditions -- Control of a System Described by a Pseudohyperbolic Equation under Conjugation Conditions -- Optimal Control of a Deformed Complicated Solid Body State En línea: http://dx.doi.org/10.1007/b104441 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35082 Optimal Control of Distributed Systems with Conjugation Conditions [documento electrónico] / Sergienko, Ivan V ; SpringerLink (Online service) ; Deineka, Vasyl S ; Shor, Naum Z . - Boston, MA : Springer US, 2005 . - XVI, 383 p : online resource. - (Nonconvex Optimization and Its Applications, ISSN 1571-568X; 75) .
ISBN : 978-0-387-24256-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Mathematical optimization Calculus of variations Variations and Optimal Control; Optimization Differential Equations Clasificación: 51 Matemáticas Resumen: This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, pseudoparabolic, hyperbolic, and pseudohyperbolic equations and with elasticity theory equation systems that have nonsmooth solutions, including discontinuous solutions. With the basis of this methodology, the monograph shows a continuous dependence of states, namely, of solutions to the enumerated boundary-value and initial boundary-value problems (including discontinuous states) and a dependence of solution traces on distributed controls and controls at sectors of n-dimensional domain boundaries and at n–1-dimensional function-state discontinuity surfaces (i.e., at mean surfaces of thin inclusions in heterogeneous media). Such an aspect provides the existence of optimal controls for the mentioned systems with J.L. Lions’ quadratic cost functionals. Besides this, the authors consider some new systems, for instance, the ones described by the conditionally correct Neumann problems with unique states on convex sets, and such states admit first-order discontinuities. These systems are also described by quartic equations with conjugation conditions, by parabolic equations with constraints that contain first-order time state derivatives in the presence of concentrated heat capacity, and by elasticity theory equations. In a number of cases, when a set of feasible controls coincides with corresponding Hilbert spaces, the authors propose to use the computational algorithms for the finite-element method. Such algorithms have the increased order of the accuracy with which optimal controls are numerically found. Audience This book is intended for specialists in applied mathematics, scientific researchers, engineers, and postgraduate students interested in optimal control of heterogeneous distributed systems with states described by boundary-value and initial boundary-value problems Nota de contenido: Control of Systems Described by Elliptic-Type Partial-Differential Equations under Conjugation Conditions -- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation under Conjugation Conditions -- Control of a System Described by a One-Dimensional Quartic Equation under Conjugation Conditions -- Control of a System Described by a Two-Dimensional Quartic Equation under Conjugation Conditions -- Control of a System Described by a Parabolic Equation under Conjugation Conditions -- Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity -- Control of a System Described by a Pseudoparabolic Equation under Conjugation Conditions -- Control of a System Described by a Hyperbolic Equation under Conjugation Conditions -- Control of a System Described by a Pseudohyperbolic Equation under Conjugation Conditions -- Optimal Control of a Deformed Complicated Solid Body State En línea: http://dx.doi.org/10.1007/b104441 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35082 Ejemplares
Signatura Medio Ubicación Sección Estado ningún ejemplar Optimal Control Problems for Partial Differential Equations on Reticulated Domains / Kogut, Peter I (2011)
Título : Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis Tipo de documento: documento electrónico Autores: Kogut, Peter I ; SpringerLink (Online service) ; Leugering, Günter R Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Systems & Control: Foundations & Applications Número de páginas: XVI, 636 p. 26 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8149-4 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations System theory Calculus of variations Applied mathematics Engineering Structural mechanics Control engineering Systems Theory, Variations and Optimal Control; Optimization Differential Equations Appl.Mathematics/Computational Methods Mechanics Clasificación: 51 Matemáticas Resumen: After over 50 years of increasing scientific interest, optimal control of partial differential equations (PDEs) has developed into a well-established discipline in mathematics with myriad applications to science and engineering. As the field has grown, so too has the complexity of the systems it describes; the numerical realization of optimal controls has become increasingly difficult, demanding ever more sophisticated mathematical tools. A comprehensive monograph on the subject, Optimal Control of Partial Differential Equations on Reticulated Domains is intended to address some of the obstacles that face researchers today, particularly with regard to multi-scale engineering applications involving hierarchies of grid-like domains. Bringing original results together with others previously scattered across the literature, it tackles computational challenges by exploiting asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs. The book consists of two parts, the first of which can be viewed as a compendium of modern optimal control theory in Banach spaces. The second part is a focused, in-depth, and self-contained study of the asymptotics of optimal control problems related to reticulated domains—the first such study in the literature. Specific topics covered in the work include: * a mostly self-contained mathematical theory of PDEs on reticulated domains; * the concept of optimal control problems for PDEs in varying such domains, and hence, in varying Banach spaces; * convergence of optimal control problems in variable spaces; * an introduction to the asymptotic analysis of optimal control problems; * optimal control problems dealing with ill-posed objects on thin periodic structures, thick periodic singular graphs, thick multi-structures with Dirichlet and Neumann boundary controls, and coefficients on reticulated structures. Serving as both a text on abstract optimal control problems and a monograph where specific applications are explored, this book is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains Nota de contenido: Introduction -- Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools -- Background Material on Asymptotic Analysis of External Problems -- Variational Methods of Optimal Control Theory -- Suboptimal and Approximate Solutions to External Problems -- Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples -- Convergence Concepts in Variable Banach Spaces -- Convergence of Sets in Variable Spaces -- Passing to the Limit in Constrained Minimization Problems -- Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions -- Suboptimal Control of Linear Steady-States Processes on Thin Periodic Structures with Mixed Boundary Controls -- Approximate Solutions of Optimal Control Problems for Ill-Posed Objects on Thin Periodic Structures -- Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures -- Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes -- Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multi-Structures with Dirichlet and Neumann Boundary Controls -- Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick Multi-Structures -- Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains -- Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8149-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33107 Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis [documento electrónico] / Kogut, Peter I ; SpringerLink (Online service) ; Leugering, Günter R . - Boston : Birkhäuser Boston, 2011 . - XVI, 636 p. 26 illus : online resource. - (Systems & Control: Foundations & Applications) .
ISBN : 978-0-8176-8149-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations System theory Calculus of variations Applied mathematics Engineering Structural mechanics Control engineering Systems Theory, Variations and Optimal Control; Optimization Differential Equations Appl.Mathematics/Computational Methods Mechanics Clasificación: 51 Matemáticas Resumen: After over 50 years of increasing scientific interest, optimal control of partial differential equations (PDEs) has developed into a well-established discipline in mathematics with myriad applications to science and engineering. As the field has grown, so too has the complexity of the systems it describes; the numerical realization of optimal controls has become increasingly difficult, demanding ever more sophisticated mathematical tools. A comprehensive monograph on the subject, Optimal Control of Partial Differential Equations on Reticulated Domains is intended to address some of the obstacles that face researchers today, particularly with regard to multi-scale engineering applications involving hierarchies of grid-like domains. Bringing original results together with others previously scattered across the literature, it tackles computational challenges by exploiting asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs. The book consists of two parts, the first of which can be viewed as a compendium of modern optimal control theory in Banach spaces. The second part is a focused, in-depth, and self-contained study of the asymptotics of optimal control problems related to reticulated domains—the first such study in the literature. Specific topics covered in the work include: * a mostly self-contained mathematical theory of PDEs on reticulated domains; * the concept of optimal control problems for PDEs in varying such domains, and hence, in varying Banach spaces; * convergence of optimal control problems in variable spaces; * an introduction to the asymptotic analysis of optimal control problems; * optimal control problems dealing with ill-posed objects on thin periodic structures, thick periodic singular graphs, thick multi-structures with Dirichlet and Neumann boundary controls, and coefficients on reticulated structures. Serving as both a text on abstract optimal control problems and a monograph where specific applications are explored, this book is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains Nota de contenido: Introduction -- Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools -- Background Material on Asymptotic Analysis of External Problems -- Variational Methods of Optimal Control Theory -- Suboptimal and Approximate Solutions to External Problems -- Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples -- Convergence Concepts in Variable Banach Spaces -- Convergence of Sets in Variable Spaces -- Passing to the Limit in Constrained Minimization Problems -- Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions -- Suboptimal Control of Linear Steady-States Processes on Thin Periodic Structures with Mixed Boundary Controls -- Approximate Solutions of Optimal Control Problems for Ill-Posed Objects on Thin Periodic Structures -- Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures -- Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes -- Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multi-Structures with Dirichlet and Neumann Boundary Controls -- Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick Multi-Structures -- Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains -- Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8149-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33107 Ejemplares
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