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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 137–148
DOI: https://doi.org/10.4213/tm3982 (Mi tm3982) 		 
Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data

F. P. Vasil'ev, L. A. Artem'eva

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm3982
Abstract: We consider an optimal control problem described by a system of linear ordinary differential equations with boundary conditions of general form defined by inequality-type constraints in the case when the input data are inaccurately specified. In general, such problems are unstable with respect to perturbations of the input data and require the development of special stable solution methods. In this paper we propose a regularized variant of the extragradient method, study its convergence, and construct a regularizing operator.
Keywords: optimal control problem, Lagrange function, Tikhonov function, saddle point, extragradient method, regularization method, regularizing operator.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00391
This work was supported by the Russian Foundation for Basic Research, project no. 18-31-00391.
Received: December 1, 2018
Revised: December 19, 2018
Accepted: January 14, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 124–135
DOI: https://doi.org/10.1134/S0081543819010085
Bibliographic databases:
Document Type: Article
UDC: 517.988.68+519.85
Language: Russian
Citation: F. P. Vasil'ev, L. A. Artem'eva, “Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 137–148; Proc. Steklov Inst. Math., 304 (2019), 124–135
Citation in format AMSBIB
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\paper Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 137--148
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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