Abstract:
This paper is devoted to the study of the properties of the adjoint variable in the relations of the Pontryagin maximum principle for a class of optimal control problems that arise in mathematical economics. This class is characterized by an infinite time interval on which a control process is considered and by a special goal functional defined by an improper integral with a discounting factor. Under a dominating discount condition, we discuss a variant of the Pontryagin maximum principle that was obtained recently by the authors and contains a description of the adjoint variable by a formula analogous to the well-known Cauchy formula for the solutions of linear differential equations. In a number of important cases, this description of the adjoint variable leads to standard transversality conditions at infinity that are usually applied when solving optimal control problems in economics. As an illustration, we analyze a conventionalized model of optimal investment policy of an enterprise.
Citation:
S. M. Aseev, A. V. Kryazhimskii, “On a Class of Optimal Control Problems Arising in Mathematical Economics”, Optimal control, Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday, Trudy Mat. Inst. Steklova, 262, MAIK Nauka/Interperiodica, Moscow, 2008, 16–31; Proc. Steklov Inst. Math., 262 (2008), 10–25
\Bibitem{AseKry08}
\by S.~M.~Aseev, A.~V.~Kryazhimskii
\paper On a~Class of Optimal Control Problems Arising in Mathematical Economics
\inbook Optimal control
\bookinfo Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2008
\vol 262
\pages 16--31
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm762}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2489724}
\zmath{https://zbmath.org/?q=an:1162.49027}
\elib{https://elibrary.ru/item.asp?id=11622611}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2008
\vol 262
\pages 10--25
\crossref{https://doi.org/10.1134/S0081543808030036}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000262228000002}
\elib{https://elibrary.ru/item.asp?id=13597141}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53849114662}
Linking options:
https://www.mathnet.ru/eng/tm762
https://www.mathnet.ru/eng/tm/v262/p16
This publication is cited in the following 9 articles:
S. A. Reshmin, M. T. Bektybaeva, “Control of acceleration of a dynamic object by the modified linear tangent law in the presence of a state constraint”, Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S168–S178
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
Rokhlin D.B., Usov A., “Rational taxation in an open access fishery model”, Arch. Control Sci., 27:1 (2017), 5–27
Derev'yanko T.O., Kyrylych V.M., “Problem of Optimal Control For a Semilinear Hyperbolic System of Equations of the First Order With Infinite Horizon Planning”, Ukr. Math. J., 67:2 (2015), 211–229
Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39
Cruz-Rivera E. Vasilieva O., “Optimal Policies Aimed at Stabilization of Populations with Logistic Growth Under Human Intervention”, Theor. Popul. Biol., 83 (2013), 123–135
S. M. Aseev, “On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 11–21
S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 67:2 (2012), 195–253
Hespeler F., “On Boundary Conditions Within the Solution of Macroeconomic Dynamic Models with Rational Expectations”, Comput. Econ., 40:3 (2012), 265–291
Citation in format AMSBIB
Contact us: