S.M. Aseev. Maximum principle for an optimal control problem with an asymptotic endpoint constraint ... P. 35-48

Under conditions characterizing the dominance of the discounting factor, a complete version of the Pontryagin maximum principle for an optimal control problem with infinite time horizon and a special asymptotic endpoint constraint is developed. Problems of this type arise in mathematical economics in the studies of growth models.

Keywords: optimal control, infinite horizon, Pontryagin maximum principle, asymptotic endpoint constraint, growth models, sustainable development

Received February 1, 2021

Revised February 15, 2021

Accepted February 22, 2021

Funding Agency: This work was supported by Russian Scientific Foundation, project 19-11-00223.

Sergey Mironovich Aseev, Dr. Phys.-Math. Sci., Corresponding member of RAS, Principal research scholar, Steklov Mathematical Institute of RAS, Gubkina 8, Moscow, 119991 Russia; Lomonosov Moscow State University, Leninskiye Gory 1, Moscow, 119991 Russia; International Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria, e-mail: aseev@mi-ras.ru

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Cite this article as: S.M.Aseev. Maximum principle for an optimal control problem with an asymptotic endpoint constraint, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 2, pp. 35–48; Proceedings of the Steklov Institute of Mathematics (Suppl. 1), 2021, Vol. 315, Suppl. 1, pp. S42–S54.