Abstract:
The authors present their recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The main distinguishing feature of the result is that the adjoint variable is explicitly specified by a formula analogous to the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the ‘standard’ transversality conditions at infinity. Moreover, it can serve as an alternative to them. Examples demonstrate the advantages of the proposed version of the maximum principle. In particular, its applications are considered to Halkin's example, to Ramsey's optimal economic growth model, and to a basic model for optimal extraction of a non-renewable resource. Also presented is an economic interpretation of the characterization obtained for the adjoint variable.
Bibliography: 62 titles.
Keywords:
optimal control, Pontryagin maximum principle, adjoint variables, transversality conditions, Ramsey model, optimal extraction of
a non-renewable resource.
The research of the first author was supported by the Russian Science Foundation under grant no. 19-11-00223.
The research of the second author was supported by the Austrian Science Fund (FWF) under grant no. P31400-N32.
Citation:
S. M. Aseev, V. M. Veliov, “Another view of the maximum principle for infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 74:6 (2019), 963–1011
\Bibitem{AseVel19}
\by S.~M.~Aseev, V.~M.~Veliov
\paper Another view of the maximum principle for infinite-horizon optimal control problems in economics
\jour Russian Math. Surveys
\yr 2019
\vol 74
\issue 6
\pages 963--1011
\mathnet{http://mi.mathnet.ru/eng/rm9915}
\crossref{https://doi.org/10.1070/RM9915}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4036769}
\zmath{https://zbmath.org/?q=an:1480.49022}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2019RuMaS..74..963A}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000518760400001}
\elib{https://elibrary.ru/item.asp?id=43765618}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087352762}
Linking options:
https://www.mathnet.ru/eng/rm9915
https://doi.org/10.1070/RM9915
https://www.mathnet.ru/eng/rm/v74/i6/p3
This publication is cited in the following 24 articles:
José E. Márquez-Prado, Onésimo Hernández-Lerma, Héctor Jasso-Fuentes, “Myopic optimal strategies for a class of continuous-time deterministic and stochastic control problems”, Systems & Control Letters, 196 (2025), 106016
José E. Márquez–Prado, Onésimo Hernández–Lerma, “Linear–State Control Problems and Differential Games: Deterministic and Stochastic Systems”, J Optim Theory Appl, 205:2 (2025)
Federico Ferraccioli, Nikolaos I. Stilianakis, Vladimir M. Veliov, “A spatial epidemic model with contact and mobility restrictions”, Mathematical and Computer Modelling of Dynamical Systems, 30:1 (2024), 284
A. A. Bazulkina, L. I. Rodina, “Teorema sravneniya dlya sistem differentsialnykh uravnenii i ee primenenie dlya otsenki srednei vremennoi vygody ot sbora resursa”, Izv. IMI UdGU, 63 (2024), 3–17
Tobias Ehring, Bernard Haasdonk, “Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems”, Adv Comput Math, 50:3 (2024)
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
D. V. Khlopin, “Ob odnoi sopryazhennoi traektorii v zadachakh upravleniya na beskonechnom promezhutke”, Tr. IMM UrO RAN, 30, no. 3, 2024, 274–292
D. V. Khlopin, “On One Adjoint Trajectory in Infinite-Horizon Control Problems”, Proc. Steklov Inst. Math., 327:S1 (2024), S155
A. A. Davydov, A. S. Platov, D. V. Tunitsky, “Existence of an Optimal Stationary Solution in the KPP Model under Nonlocal Competition”, Proc. Steklov Inst. Math., 327:S1 (2024), S66
S. M. Aseev, “The Pontryagin maximum principle for optimal control problem with an asymptotic endpoint constraint under weak regularity assumptions”, J. Math. Sci., 270:4 (2023), 531
A. O. Belyakov, “Optimal accumulation of factors with linear-homogeneous production functions on infinite time horizon”, J. Math. Sci., 269:6 (2023), 755
Yu. Zheng, J. 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, 49 pp.
D. Khlopin, “Necessary conditions in infinite-horizon control problems that need no asymptotic assumptions”, Set-Valued Var. Anal., 31:1 (2023), 8
S. M. Aseev, “Conditional cost function and necessary optimality conditions for infinite horizon optimal control problems”, Dokl. Math., 108:3 (2023), 425–430
S. M. Aseev, “Necessary conditions for the optimality and sustainability of solutions in infinite-horizon optimal control problems”, Mathematics, 11:18 (2023), 3851
A. Shananin, N. Trusov, “The group behaviour modelling of workers in the labor market”, Russian Journal of Numerical Analysis and Mathematical Modelling, 38:4 (2023), 219
N. V. Trusov, A. A. Shananin, “Mathematical model of human capital dynamics”, Comput. Math. Math. Phys., 63:10 (2023), 1942–1954
A. Davydov, E. Vinnikov, “Optimal cyclic dynamic of distributed population under permanent and impulse harvesting”, Dynamic Control and Optimization, Springer Proceedings in Mathematics & Statistics, 407, 2022, 101–112
L. Lehmann, “Hamilton’s rule, the evolution of behavior rules and the wizardry of control theory”, Journal of Theoretical Biology, 555 (2022), 111282
T. V. Bogachev, S. N. Popova, “On Optimization of Tax Functions”, Math. Notes, 109:2 (2021), 163–170
Citation in format AMSBIB
Contact us: