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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 65–75
DOI: https://doi.org/10.4213/tm4092 (Mi tm4092) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems

Anton O. Belyakovabcd

a Moscow School of Economics, Lomonosov Moscow State University, Leninskie Gory 1, str. 61, Moscow, 119234 Russia
b National Research Nuclear University “MEPhI,” Kashirskoe sh. 31, Moscow, 115409 Russia
c National University of Science and Technology “MISiS,” Leninskii pr. 4, Moscow, 119049 Russia
d Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418 Russia
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DOI: https://doi.org/10.4213/tm4092
Abstract: We consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied and provide appropriate examples. The sufficient conditions are shown to be both necessary and sufficient when the Hamiltonian is linear with respect to state and control. We obtain a new form of sufficient optimality conditions in the case when the Hamiltonian is neither concave nor differentiable with respect to control.
Funding agency Grant number
Russian Science Foundation 19-11-00223
This work is supported by the Russian Science Foundation under grant 19-11-00223.
Received: September 27, 2019
Revised: January 21, 2020
Accepted: February 25, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 56–66
DOI: https://doi.org/10.1134/S0081543820010058
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
Language: Russian
Citation: Anton O. Belyakov, “On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 65–75; Proc. Steklov Inst. Math., 308 (2020), 56–66
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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