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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 208, Pages 63–78
DOI: https://doi.org/10.36535/0233-6723-2022-208-63-78 (Mi into995) 		 
The Lagrange principle and the Pontryagin maximum principle in ill-posed optimal control problems

M. I. Suminab

a Tambov State University named after G.R. Derzhavin
b National Research Lobachevsky State University of Nizhny Novgorod
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DOI: https://doi.org/10.36535/0233-6723-2022-208-63-78
Abstract: We consider the regularization of the classical optimality conditions—the Lagrange principle and the Pontryagin maximum principle—in a convex optimal control problem for a parabolic equation with distributed and boundary controls, and also with a finite number functional equality constraints given by ‘`point’ functionals nondifferentiable in the Fréchet sense, which are the values of the solution of the third initial-boundary-value problem for the specified equation at preselected fixed (possibly boundary) points of the cylindrical domain of the independent variables.
Keywords: convex optimal control, parabolic equation, boundary control, Fréchet nondifferentiable functional, Steklov averaging, minimizing sequence, dual regularization, regularizing algorithm, Lagrange principle, Pontryagin maximum principle.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00199a
This work was supported by the Russian Foundation for Basic Research (project No. 20-01-00199_a).
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 49K20, 49N15, 47A52
Language: Russian
Citation: M. I. Sumin, “The Lagrange principle and the Pontryagin maximum principle in ill-posed optimal control problems”, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 208, VINITI, Moscow, 2022, 63–78
Citation in format AMSBIB
\Bibitem{Sum22}
\by M.~I.~Sumin
\paper The Lagrange principle and the Pontryagin maximum principle in ill-posed optimal control problems
\inbook Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 208
\pages 63--78
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into995}
\crossref{https://doi.org/10.36535/0233-6723-2022-208-63-78}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1040047}
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