Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 1, Pages 25–49
DOI: https://doi.org/10.7868/S0044466914010141
(Mi zvmmf9971)
 

This article is cited in 23 scientific papers (total in 23 papers)

Stable sequential convex programming in a Hilbert space and its application for solving unstable problems

M. I. Sumin

Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia
References:
Abstract: A parametric convex programming problem with an operator equality constraint and a finite set of functional inequality constraints is considered in a Hilbert space. The instability of this problem and, as a consequence, the instability of the classical Lagrange principle for it is closely related to its regularity and the subdifferentiability properties of the value function in the optimization problem. A sequential Lagrange principle in nondifferential form is proved for the indicated convex programming problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. It is shown that the classical Lagrange principle in this problem can be naturally treated as a limiting variant of its stable sequential counterpart. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimal control problems and inverse problems is discussed. For two illustrative problems of these kinds, the corresponding stable Lagrange principles are formulated in sequential form.
Key words: convex programming, parametric problem, perturbation method, stability, sequential optimization, minimizing sequence, Lagrange principle in nondifferential and differential forms, Kuhn–Tucker theorem, duality, regularization, unstable problems.
Received: 02.07.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 1, Pages 22–44
DOI: https://doi.org/10.1134/S0965542514010138
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: M. I. Sumin, “Stable sequential convex programming in a Hilbert space and its application for solving unstable problems”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 25–49; Comput. Math. Math. Phys., 54:1 (2014), 22–44
Citation in format AMSBIB
\Bibitem{Sum14}
\by M.~I.~Sumin
\paper Stable sequential convex programming in a Hilbert space and its application for solving unstable problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 1
\pages 25--49
\mathnet{http://mi.mathnet.ru/zvmmf9971}
\crossref{https://doi.org/10.7868/S0044466914010141}
\elib{https://elibrary.ru/item.asp?id=20991861}
\transl
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 1
\pages 22--44
\crossref{https://doi.org/10.1134/S0965542514010138}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000332109500003}
\elib{https://elibrary.ru/item.asp?id=21866671}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84894636380}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf9971
  • https://www.mathnet.ru/eng/zvmmf/v54/i1/p25
  • This publication is cited in the following 23 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
    Statistics & downloads:
    Abstract page:674
    Full-text PDF :98
    References:71
    First page:15
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024