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 Mat. Zametki, 2004, Volume 76, Issue 6, Pages 893–904 (Mi mz161)

Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems

S. Ya. Serovaĭskiĭ

Al-Farabi Kazakh National University

Abstract: We consider an abstract optimal control problem with additional constraints and nonsmooth terms, but without the requirement that both the state equation on the set of admissible controls and the extremum problem be solvable. We use the approximate penalty method proposed here to find an approximate (in the weak sense) solution of the problem. As an example, we consider the optimal control problem for a singular nonlinear elliptic type equation.

DOI: https://doi.org/10.4213/mzm161

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English version:
Mathematical Notes, 2004, 76:6, 834–843

Bibliographic databases:

UDC: 517.977

Citation: S. Ya. Serovaǐskiǐ, “Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems”, Mat. Zametki, 76:6 (2004), 893–904; Math. Notes, 76:6 (2004), 834–843

Citation in format AMSBIB
\Bibitem{Ser04} \by S.~Ya.~Serova{\v\i}ski{\v\i} \paper Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems \jour Mat. Zametki \yr 2004 \vol 76 \issue 6 \pages 893--904 \mathnet{http://mi.mathnet.ru/mz161} \crossref{https://doi.org/10.4213/mzm161} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2127500} \zmath{https://zbmath.org/?q=an:1098.49029} \transl \jour Math. Notes \yr 2004 \vol 76 \issue 6 \pages 834--843 \crossref{https://doi.org/10.1023/B:MATN.0000049683.80550.12} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000226356700025} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-10344230991} 

• http://mi.mathnet.ru/eng/mz161
• https://doi.org/10.4213/mzm161
• http://mi.mathnet.ru/eng/mz/v76/i6/p893

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Serovaiskii, SY, “Optimal control of a singular evolution equation with a nonsmooth operator and fixed terminal state”, Differential Equations, 43:2 (2007), 259
2. Benharrat M., Torres D.F.M., “Optimal Control With Time Delays Via the Penalty Method”, Math. Probl. Eng., 2014, 250419
3. S. Ya. Serovaǐskiǐ, “Optimal Control of Singular Stationary Systems with Phase Constraints and State Variation”, Math. Notes, 97:5 (2015), 774–778
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