Functional analysis, calculus of variations and optimal control
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 o...
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
London :
Springer London
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2013. |
| Col·lecció: | Graduate Texts in Mathematics
264 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Functional analysis, calculus of variations and optimal control, Francis Clarke, 2013, London, Springer, 1 vol. (XIV-591 p.), Graduate texts in mathematics, 978-1-4471-4819-7 • Functional analysis, calculus of variations and optimal control, Francis Clarke, 2013, London, Springer, 1 vol. (XIV-591 p.), Graduate texts in mathematics, 978-1-4471-4819-7 • Functional Analysis, Calculus of Variations and Optimal Control, Texte imprimé, 9781447148210 • Functional analysis, calculus of variations and optimal control, Francis Clarke, 2013, London, Springer, 1 vol. (591 p.), Graduate texts in mathematics, 978-1-4471-6210-0 |
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| 100 | 1 | |a Clarke, Frank H., |d 1948-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Functional analysis, calculus of variations and optimal control |c Francis Clarke. |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 264 |x 2197-5612 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a 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 | |
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Analyse fonctionnelle | ||
| 650 | |a Calcul des variations | ||
| 650 | |a Théorie de la commande | ||
| 776 | 0 | |0 168544679 |t Functional analysis, calculus of variations and optimal control |f Francis Clarke |d 2013 |c London |n Springer |p 1 vol. (XIV-591 p.) |s Graduate texts in mathematics |z 978-1-4471-4819-7 | |
| 776 | 0 | |0 168544679 |t Functional analysis, calculus of variations and optimal control |f Francis Clarke |d 2013 |c London |n Springer |p 1 vol. (XIV-591 p.) |s Graduate texts in mathematics |z 978-1-4471-4819-7 | |
| 776 | 0 | |t Functional Analysis, Calculus of Variations and Optimal Control |b Texte imprimé |z 9781447148210 | |
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