Variational Calculus and Optimal Control: Optimization with Elementary Convexity
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
New York, NY
Springer New York
1996
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Ausgabe: | Second Edition |
Schriftenreihe: | Undergraduate Texts in Mathematics
|
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | Although the calculus of variations has ancient origins in questions of Ar istotle and Zenodoros, its mathematical principles first emerged in the post calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob tained through variational principles may provide the only valid mathemati cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning |
Beschreibung: | 1 Online-Ressource (XV, 462 p) |
ISBN: | 9781461207375 9781461268871 |
ISSN: | 0172-6056 |
DOI: | 10.1007/978-1-4612-0737-5 |
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author | Troutman, John L. |
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discipline | Mathematik |
doi_str_mv | 10.1007/978-1-4612-0737-5 |
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spelling | Troutman, John L. Verfasser aut Variational Calculus and Optimal Control Optimization with Elementary Convexity by John L. Troutman Second Edition New York, NY Springer New York 1996 1 Online-Ressource (XV, 462 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 Although the calculus of variations has ancient origins in questions of Ar istotle and Zenodoros, its mathematical principles first emerged in the post calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob tained through variational principles may provide the only valid mathemati cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Konvexe Funktion (DE-588)4139679-0 s 1\p DE-604 Optimale Kontrolle (DE-588)4121428-6 s Konvexe Optimierung (DE-588)4137027-2 s 2\p DE-604 3\p DE-604 4\p DE-604 https://doi.org/10.1007/978-1-4612-0737-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Troutman, John L. Variational Calculus and Optimal Control Optimization with Elementary Convexity Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung (DE-588)4062355-5 gnd Konvexe Funktion (DE-588)4139679-0 gnd Konvexe Optimierung (DE-588)4137027-2 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
subject_GND | (DE-588)4062355-5 (DE-588)4139679-0 (DE-588)4137027-2 (DE-588)4121428-6 |
title | Variational Calculus and Optimal Control Optimization with Elementary Convexity |
title_auth | Variational Calculus and Optimal Control Optimization with Elementary Convexity |
title_exact_search | Variational Calculus and Optimal Control Optimization with Elementary Convexity |
title_full | Variational Calculus and Optimal Control Optimization with Elementary Convexity by John L. Troutman |
title_fullStr | Variational Calculus and Optimal Control Optimization with Elementary Convexity by John L. Troutman |
title_full_unstemmed | Variational Calculus and Optimal Control Optimization with Elementary Convexity by John L. Troutman |
title_short | Variational Calculus and Optimal Control |
title_sort | variational calculus and optimal control optimization with elementary convexity |
title_sub | Optimization with Elementary Convexity |
topic | Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung (DE-588)4062355-5 gnd Konvexe Funktion (DE-588)4139679-0 gnd Konvexe Optimierung (DE-588)4137027-2 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
topic_facet | Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung Konvexe Funktion Konvexe Optimierung Optimale Kontrolle |
url | https://doi.org/10.1007/978-1-4612-0737-5 |
work_keys_str_mv | AT troutmanjohnl variationalcalculusandoptimalcontroloptimizationwithelementaryconvexity |