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Russian Mathematical Surveys, 2013, Volume 68, Issue 3, Pages 401–433
DOI: https://doi.org/10.1070/RM2013v068n03ABEH004838 (Mi rm9525) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Lagrange's principle in extremum problems with constraints

E. R. Avakova, G. G. Magaril-Il'yaevbc, V. M. Tikhomirovc

a Institute of Control Sciences of the Russian Academy of Sciences
b Institute for Information Transmission Problems of the Russian Academy of Sciences
c Moscow State University
English version PDF (763 kB) Citations (19)
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DOI: https://doi.org/10.1070/RM2013v068n03ABEH004838
Abstract: In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a ‘Lagrangian approach’ to problems where regularity is absent and classical approaches are meaningless.
Bibliography: 33 titles.
Keywords: extremum problem, optimal control, phase constraints, mix, controllability, abnormality.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00188
11-01-00529
Received: 11.10.2012
Russian version:
Uspekhi Matematicheskikh Nauk, 2013, Volume 68, Issue 3(411), Pages 5–38
DOI: https://doi.org/10.4213/rm9525
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: Primary 49J40; Secondary 49M05
Language: English
Original paper language: Russian
Citation: E. R. Avakov, G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Lagrange's principle in extremum problems with constraints”, Uspekhi Mat. Nauk, 68:3(411) (2013), 5–38; Russian Math. Surveys, 68:3 (2013), 401–433
Citation in format AMSBIB
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    • This publication is cited in the following 19 articles:
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    References:139
    First page:134
     
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