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Título : Calculus of Variations, Classical and Modern Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; R. Conti Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: C.I.M.E. Summer Schools num. 39 Número de páginas: 369 p. 30 illus Il.: online resource ISBN/ISSN/DL: 978-3-642-11042-9 Idioma : Inglés (eng) Palabras clave: Mathematics Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: A. Blaquière: Quelques aspects géométriques des processus optimaux.- C. Castaing: Quelques problèmes de mesurabilité liés à la théorie des commandes.- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space.- H. Halkin: Optimal control as programming in infinite dimensional spaces.- C. Olech: The range of integrals of a certain class vector-valued functions.- E. Rothe: Weak topology and calculus of variations.- E.O. Roxin: Problems about the set of attainability Nota de contenido: A. Blaquière: Quelques aspects géométriques des processus optimaux -- C. Castaing: Quelques problèmes de mesurabilité liés à la théorie des commandes -- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space -- H. Halkin: Optimal control as programming in infinite dimensional spaces -- C. Olech: The range of integrals of a certain class vector-valued functions -- E. Rothe: Weak topology and calculus of variations -- E.O. Roxin: Problems about the set of attainability En línea: http://dx.doi.org/10.1007/978-3-642-11042-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33331 Calculus of Variations, Classical and Modern [documento electrónico] / SpringerLink (Online service) ; R. Conti . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - 369 p. 30 illus : online resource. - (C.I.M.E. Summer Schools; 39) .
ISBN : 978-3-642-11042-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: A. Blaquière: Quelques aspects géométriques des processus optimaux.- C. Castaing: Quelques problèmes de mesurabilité liés à la théorie des commandes.- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space.- H. Halkin: Optimal control as programming in infinite dimensional spaces.- C. Olech: The range of integrals of a certain class vector-valued functions.- E. Rothe: Weak topology and calculus of variations.- E.O. Roxin: Problems about the set of attainability Nota de contenido: A. Blaquière: Quelques aspects géométriques des processus optimaux -- C. Castaing: Quelques problèmes de mesurabilité liés à la théorie des commandes -- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space -- H. Halkin: Optimal control as programming in infinite dimensional spaces -- C. Olech: The range of integrals of a certain class vector-valued functions -- E. Rothe: Weak topology and calculus of variations -- E.O. Roxin: Problems about the set of attainability En línea: http://dx.doi.org/10.1007/978-3-642-11042-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33331 Ejemplares
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Título : Direct Methods in the Calculus of Variations Tipo de documento: documento electrónico Autores: Bernard Dacorogna ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 78 Número de páginas: XII, 622 p Il.: online resource ISBN/ISSN/DL: 978-0-387-55249-1 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Calculus of variations Differential Equations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This book studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added. This monograph will appeal to researchers and graduate students in mathematics and engineering Nota de contenido: Convex analysis and the scalar case -- Convex sets and convex functions -- Lower semicontinuity and existence theorems -- The one dimensional case -- Quasiconvex analysis and the vectorial case -- Polyconvex, quasiconvex and rank one convex functions -- Polyconvex, quasiconvex and rank one convex envelopes -- Polyconvex, quasiconvex and rank one convex sets -- Lower semi continuity and existence theorems in the vectorial case -- Relaxation and non-convex problems -- Relaxation theorems -- Implicit partial differential equations -- Existence of minima for non-quasiconvex integrands -- Miscellaneous -- Function spaces -- Singular values -- Some underdetermined partial differential equations -- Extension of Lipschitz functions on Banach spaces En línea: http://dx.doi.org/10.1007/978-0-387-55249-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34152 Direct Methods in the Calculus of Variations [documento electrónico] / Bernard Dacorogna ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XII, 622 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 78) .
ISBN : 978-0-387-55249-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Calculus of variations Differential Equations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This book studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added. This monograph will appeal to researchers and graduate students in mathematics and engineering Nota de contenido: Convex analysis and the scalar case -- Convex sets and convex functions -- Lower semicontinuity and existence theorems -- The one dimensional case -- Quasiconvex analysis and the vectorial case -- Polyconvex, quasiconvex and rank one convex functions -- Polyconvex, quasiconvex and rank one convex envelopes -- Polyconvex, quasiconvex and rank one convex sets -- Lower semi continuity and existence theorems in the vectorial case -- Relaxation and non-convex problems -- Relaxation theorems -- Implicit partial differential equations -- Existence of minima for non-quasiconvex integrands -- Miscellaneous -- Function spaces -- Singular values -- Some underdetermined partial differential equations -- Extension of Lipschitz functions on Banach spaces En línea: http://dx.doi.org/10.1007/978-0-387-55249-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34152 Ejemplares
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Título : Functional Analysis, Calculus of Variations and Optimal Control Tipo de documento: documento electrónico Autores: Francis Clarke ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 264 Número de páginas: XIV, 591 p. 24 illus., 8 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4471-4820-3 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis System theory Calculus of variations Mathematical optimization Analysis Variations and Optimal Control; Optimization Continuous Systems Theory, Control Clasificación: 51 Matemáticas Resumen: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields Nota de contenido: Normed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV En línea: http://dx.doi.org/10.1007/978-1-4471-4820-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32194 Functional Analysis, Calculus of Variations and Optimal Control [documento electrónico] / Francis Clarke ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - XIV, 591 p. 24 illus., 8 illus. in color : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 264) .
ISBN : 978-1-4471-4820-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis System theory Calculus of variations Mathematical optimization Analysis Variations and Optimal Control; Optimization Continuous Systems Theory, Control Clasificación: 51 Matemáticas Resumen: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields Nota de contenido: Normed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV En línea: http://dx.doi.org/10.1007/978-1-4471-4820-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32194 Ejemplares
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Título : Modern Methods in the Calculus of Variations: Lp Spaces Tipo de documento: documento electrónico Autores: Irene Fonseca ; SpringerLink (Online service) ; Giovanni Leoni Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XIV, 600 p Il.: online resource ISBN/ISSN/DL: 978-0-387-69006-3 Idioma : Inglés (eng) Palabras clave: Physics Mathematical analysis Analysis (Mathematics) Partial differential equations Applied mathematics Engineering Calculus of variations Continuum mechanics Physics, general Variations and Optimal Control; Optimization Mechanics Materials Applications Mathematics Differential Equations Clasificación: 51 Matemáticas Resumen: This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science Nota de contenido: Measure Theory and Lp Spaces -- Measures -- Lp Spaces -- The Direct Method and Lower Semicontinuity -- The Direct Method and Lower Semicontinuity -- ConvexAnalysis -- Functionals Defined on Lp -- Integrands f = f (z) -- Integrands f = f (x, z) -- Integrands f = f (x, u, z) -- Young Measures En línea: http://dx.doi.org/10.1007/978-0-387-69006-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34511 Modern Methods in the Calculus of Variations: Lp Spaces [documento electrónico] / Irene Fonseca ; SpringerLink (Online service) ; Giovanni Leoni . - New York, NY : Springer New York, 2007 . - XIV, 600 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-0-387-69006-3
Idioma : Inglés (eng)
Palabras clave: Physics Mathematical analysis Analysis (Mathematics) Partial differential equations Applied mathematics Engineering Calculus of variations Continuum mechanics Physics, general Variations and Optimal Control; Optimization Mechanics Materials Applications Mathematics Differential Equations Clasificación: 51 Matemáticas Resumen: This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science Nota de contenido: Measure Theory and Lp Spaces -- Measures -- Lp Spaces -- The Direct Method and Lower Semicontinuity -- The Direct Method and Lower Semicontinuity -- ConvexAnalysis -- Functionals Defined on Lp -- Integrands f = f (z) -- Integrands f = f (x, z) -- Integrands f = f (x, u, z) -- Young Measures En línea: http://dx.doi.org/10.1007/978-0-387-69006-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34511 Ejemplares
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Título : Turnpike Properties in the Calculus of Variations and Optimal Control Tipo de documento: documento electrónico Autores: SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2006 Colección: Nonconvex Optimization and Its Applications, ISSN 1571-568X num. 80 Número de páginas: XXII, 396 p Il.: online resource ISBN/ISSN/DL: 978-0-387-28154-4 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical optimization Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics Nota de contenido: Infinite Horizon Variational Problems -- Extremals of Nonautonomous Problems -- Extremals of Autonomous Problems -- Infinite Horizon Autonomous Problems -- Turnpike for Autonomous Problems -- Linear Periodic Control Systems -- Linear Systems with Nonperiodic Integrands -- Discrete-Time Control Systems -- Control Problems in Hilbert Spaces -- A Class of Differential Inclusions -- Convex Processes -- A Dynamic Zero-Sum Game En línea: http://dx.doi.org/10.1007/0-387-28154-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34747 Turnpike Properties in the Calculus of Variations and Optimal Control [documento electrónico] / SpringerLink (Online service) . - Boston, MA : Springer US, 2006 . - XXII, 396 p : online resource. - (Nonconvex Optimization and Its Applications, ISSN 1571-568X; 80) .
ISBN : 978-0-387-28154-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical optimization Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics Nota de contenido: Infinite Horizon Variational Problems -- Extremals of Nonautonomous Problems -- Extremals of Autonomous Problems -- Infinite Horizon Autonomous Problems -- Turnpike for Autonomous Problems -- Linear Periodic Control Systems -- Linear Systems with Nonperiodic Integrands -- Discrete-Time Control Systems -- Control Problems in Hilbert Spaces -- A Class of Differential Inclusions -- Convex Processes -- A Dynamic Zero-Sum Game En línea: http://dx.doi.org/10.1007/0-387-28154-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34747 Ejemplares
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