S. M. Aseev, A. V. Kryazhimskii, “The Pontryagin Maximum Principle and Optimal Economic Growth Problems”, Trudy Mat. Inst. Steklova, 257, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 3–271; Proc. Steklov Inst. Math., 257 (2007), 1

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 257, Pages 3–271 (Mi tm470)

This article is cited in 148 scientific papers (total in 148 papers)

The Pontryagin Maximum Principle and Optimal Economic Growth Problems

S. M. Aseev^ab, A. V. Kryazhimskii^ab

^a Steklov Mathematical Institute, Russian Academy of Sciences
^b International Institute for Applied Systems Analysis

Full-text PDF (1897 kB) Citations (148)

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Abstract: This monograph is devoted to the theory of the Pontryagin maximum principle as applied to a special class of optimal control problems that arise in economics when studying economic growth processes. The first chapter presents a new approximation approach that leads to a complete set of necessary optimality conditions in the form of the Pontryagin maximum principle. The attention is focused on the characterization of the behavior of the adjoint variable and the Hamiltonian of a problem at infinity. In the second chapter, the approach proposed is applied to a problem of optimal dynamical allocation of labor resources in the endogenous economic growth theory.
The monograph is addressed to a wide circle of scientists, postgraduates, and students who are interested in the theory of the Pontryagin maximum principle and its applications in economics.

Received in February 2007

English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 257, Pages 1–255
DOI: https://doi.org/10.1134/S0081543807020010

Bibliographic databases:

Document Type: Book

UDC: 517.977.5+519.86

Language: Russian

Citation: S. M. Aseev, A. V. Kryazhimskii, “The Pontryagin Maximum Principle and Optimal Economic Growth Problems”, Trudy Mat. Inst. Steklova, 257, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 3–271; Proc. Steklov Inst. Math., 257 (2007), 1–255

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm470

https://www.mathnet.ru/eng/tm/v257/p3

This publication is cited in the following 148 articles:

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A. S. Aseev, S. P. Samsonov, “On the problem of optimal stimulation of demand”, Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S33–S47
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A. A. Davydov, A. S. Platov, D. V. Tunitskii, “Suschestvovanie optimalnogo statsionarnogo resheniya v KPP-modeli pri nelokalnoi konkurentsii”, Tr. IMM UrO RAN, 30, no. 3, 2024, 113–121
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G. S. Parastaev, A. A. Shananin, “Ramsey's Conjecture of Social Stratification as Fisher's Selection Principle”, Comput. Math. and Math. Phys., 64:12 (2024), 2952
D. V. Khlopin, “On One Adjoint Trajectory in Infinite-Horizon Control Problems”, Proc. Steklov Inst. Math., 327:S1 (2024), S155
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Yueyang Zheng, Jingtao Shi, “The maximum principle for discounted optimal control of partially observed forward-backward stochastic systems with jumps on infinite horizon”, ESAIM: COCV, 29 (2023), 34
Dmitry Khlopin, “Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions”, Set-Valued Var. Anal, 31:1 (2023)
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S. M. Aseev, “The Pontryagin maximum principle for optimal control problem with an asymptotic endpoint constraint under weak regularity assumptions”, J. Math. Sci. (N.Y.), 270:4 (2023), 531–546
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Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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