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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 268, Pages 64–75 (Mi tm2876)  

This article is cited in 9 scientific papers (total in 9 papers)

The Pontryagin maximum principle and a unified theory of dynamic optimization

F. Clarke

CNRS, UMR 5208, Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, France
Full-text PDF (203 kB) Citations (9)
References:
Abstract: The Pontryagin maximum principle is the central result of optimal control theory. In the half-century since its appearance, the underlying theorem has been generalized, strengthened, extended, proved and reinterpreted in a variety of ways. We review in this article one of the principal approaches to obtaining the maximum principle in a powerful and unified context, focusing upon recent results that represent the culmination of over thirty years of progress using the methodology of nonsmooth analysis. We illustrate the novel features of this theory, as well as its versatility, by introducing a far-reaching new theorem that bears upon the currently active subject of mixed constraints in optimal control.
Received in April 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 268, Pages 58–69
DOI: https://doi.org/10.1134/S0081543810010062
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: English
Citation: F. Clarke, “The Pontryagin maximum principle and a unified theory of dynamic optimization”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 64–75; Proc. Steklov Inst. Math., 268 (2010), 58–69
Citation in format AMSBIB
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\paper The Pontryagin maximum principle and a~unified theory of dynamic optimization
\inbook Differential equations and topology.~I
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
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\vol 268
\pages 64--75
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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