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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 41–57 (Mi timm1084)  

This article is cited in 8 scientific papers (total in 8 papers)

Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions

S. M. Aseevab, V. M. Veliovc

a Steklov Mathematical Institute, Gubkina str. 8, Moscow, 119991, Russia
b International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg, A-2361, Austria
c Institute of Mathematical Methods in Economics, Vienna University of Technology, Argentinier str. 8/E105-4, A-1040 Vienna, Austria

Abstract: The paper deals with first order necessary optimality conditions for a class of infinite-horizon optimal control problems that arise in economic applications. Neither convergence of the integral utility functional nor local boundedness of the optimal control is assumed. Using the classical needle variations technique we develop a normal form version of the Pontryagin maximum principle with an explicitly specified adjoint variable under weak regularity assumptions. The result generalizes some previous results in this direction. An illustrative economical example is presented.

Keywords: infinite horizon, Pontryagin maximum principle, transversality conditions, weak regularity assumptions.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12446-ofi-m2
Austrian Science Fund P 26640-N25
The first author was supported in part by the Russian Foundation for Basic Research under grant No. 13-01-12446-ofi-m2. The second author was supported by the Austrian Science Foundation (FWF) under grant P 26640-N25.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 291, suppl. 1, 22–39

Bibliographic databases:

Document Type: Article
UDC: 517.97
Received: 08.06.2014
Language: English

Citation: S. M. Aseev, V. M. Veliov, “Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 41–57; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39

Citation in format AMSBIB
\by S.~M.~Aseev, V.~M.~Veliov
\paper Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 3
\pages 41--57
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 291
\issue , suppl. 1
\pages 22--39

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    This publication is cited in the following articles:
    1. S. M. Aseev, “Adjoint variables and intertemporal prices in infinite-horizon optimal control problems”, Proc. Steklov Inst. Math., 290:1 (2015), 223–237  mathnet  crossref  crossref  zmath  isi  elib  elib
    2. S. M. Aseev, “On the boundedness of optimal controls in infinite-horizon problems”, Proc. Steklov Inst. Math., 291 (2015), 38–48  mathnet  crossref  crossref  isi  elib
    3. N. Tauchnitz, “The Pontryagin maximum principle for nonlinear optimal control problems with infinite horizon”, J. Optim. Theory Appl., 167:1 (2015), 27–48  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. M. Aseev, “Existence of an optimal control in infinite-horizon problems with unbounded set of control constraints”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 1–10  mathnet  crossref  crossref  mathscinet  isi  elib
    5. P. Cannarsa, H. Frankowska, “Infinite horizon optimal control: transversality conditions and sensitivity relations”, Proceedings of the American Control Conference, 2017 American Control Conference (ACC), IEEE, 2017, 2630–2635  crossref  isi  scopus
    6. P. Cannarsa, H. Frankowska, “Value function, relaxation, and transversality conditions in infinite horizon optimal control”, J. Math. Anal. Appl., 457:2 (2018), 1188–1217  crossref  mathscinet  zmath  isi  scopus
    7. A. Bondarev, A. Greiner, “Catching-up and falling behind: effects of learning in an R&D differential game with spillovers”, J. Econ. Dyn. Control, 91 (2018), 134–156  crossref  mathscinet  zmath  isi  scopus
    8. S. M. Aseev, K. O. Besov, S. Yu. Kaniovski, “Optimal Policies in the Dasgupta–Heal–Solow–Stiglitz Model under Nonconstant Returns to Scale”, Proc. Steklov Inst. Math., 304 (2019), 74–109  mathnet  crossref  crossref  isi  elib
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