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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 11, Pages 1987–2000 (Mi zvmmf380)  
This article is cited in 5 scientific papers (total in 6 papers)

New numerical methods and some applied aspects of the $p$-regularity theory

O. A. Brezhnevaa, Yu. G. Evtushenkob, A. A. Tret'yakovbcd

a Department of Mathematics and Statistics, Miami University, 123 Bachelor Hall, Oxford, Ohio 45056, USA
b Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
c University of Podlasie, 08-110 Siedlce, Poland
d System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
Full-text PDF (1408 kB) Citations (6)
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Abstract: The theory of $p$-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu. G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the $p$-factor method for solving ODEs with a small parameter.
Key words: $p$-regularity theory, method of modified Lagrangian functions, optimization problems, singular ODE, implicit function theorem in the singular case.
Received: 31.03.2006
Revised: 06.06.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 11, Pages 1896–1909
DOI: https://doi.org/10.1134/S0965542506110066
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: O. A. Brezhneva, Yu. G. Evtushenko, A. A. Tret'yakov, “New numerical methods and some applied aspects of the $p$-regularity theory”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 1987–2000; Comput. Math. Math. Phys., 46:11 (2006), 1896–1909
Citation in format AMSBIB
\Bibitem{BreEvtTre06}
\by O.~A.~Brezhneva, Yu.~G.~Evtushenko, A.~A.~Tret'yakov
\paper New numerical methods and some applied aspects of the $p$-regularity theory
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 11
\pages 1987--2000
\mathnet{http://mi.mathnet.ru/zvmmf380}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2304071}
\elib{https://elibrary.ru/item.asp?id=9310392}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 11
\pages 1896--1909
\crossref{https://doi.org/10.1134/S0965542506110066}
\elib{https://elibrary.ru/item.asp?id=13505391}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845348195}
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  • https://www.mathnet.ru/eng/zvmmf/v46/i11/p1987
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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