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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 262, Pages 156–177 (Mi tm771)  
This article is cited in 6 scientific papers (total in 6 papers)

Newton's Method, Differential Equations, and the Lagrangian Principle for Necessary Extremum Conditions

G. G. Magaril-Il'yaev, V. M. Tikhomirov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (316 kB) Citations (6)
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Abstract: We show how one can use a modified Newton's method to prove existence and uniqueness theorems for solutions of differential equations and theorems on the continuous and differentiable dependence of these solutions on the initial data and parameters and to derive necessary conditions for an extremum in various extremum problems (from the origins to our days).
Received in February 2008
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 262, Pages 149–169
DOI: https://doi.org/10.1134/S0081543808030127
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Newton's Method, Differential Equations, and the Lagrangian Principle for Necessary Extremum Conditions”, Optimal control, Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday, Trudy Mat. Inst. Steklova, 262, MAIK Nauka/Interperiodica, Moscow, 2008, 156–177; Proc. Steklov Inst. Math., 262 (2008), 149–169
Citation in format AMSBIB
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\paper Newton's Method, Differential Equations, and the Lagrangian Principle for Necessary Extremum Conditions
\inbook Optimal control
\bookinfo Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday
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\pages 156--177
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 6 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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