Abstract:
The properties of adjoint variables involved in the relations of the Pontryagin maximum principle are investigated for a class of infinite-horizon optimal control problems that arise in the study of economic growth processes. New formulations of the maximum principle in terms of intertemporal prices and the conditional value of the capital are established. Several illustrative examples are considered.
Citation:
S. M. Aseev, “Adjoint variables and intertemporal prices in infinite-horizon optimal control problems”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Trudy Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 239–253; Proc. Steklov Inst. Math., 290:1 (2015), 223–237
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\by S.~M.~Aseev
\paper Adjoint variables and intertemporal prices in infinite-horizon optimal control problems
\inbook Modern problems of mathematics, mechanics, and mathematical physics
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 290
\pages 239--253
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 290
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\pages 223--237
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Linking options:
https://www.mathnet.ru/eng/tm3655
https://doi.org/10.1134/S0371968515030206
https://www.mathnet.ru/eng/tm/v290/p239
This publication is cited in the following 10 articles:
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
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
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
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
K. O. Besov, “On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems”, Math. Notes, 103:2 (2018), 167–174
S. M. Aseev, “An existence result for infinite-horizon optimal control problem with unbounded set of control constraints”, IFAC PAPERSONLINE, 51:32 (2018), 281–285
S. Aseev, T. Manzoor, “Optimal exploitation of renewable resources: lessons in sustainability from an optimal growth model of natural resource consumption”, Control Systems and Mathematical Methods in Economics: Essays in Honor of Vladimir M. Veliov, Lecture Notes in Economics and Mathematical Systems, 687, ed. G. Feichtinger, R. Kovacevic, G. Tragler, Springer-Verlag Berlin, 2018, 221–245
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
S. M. Aseev, “On the boundedness of optimal controls in infinite-horizon problems”, Proc. Steklov Inst. Math., 291 (2015), 38–48
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