Abstract:
For a class of infinite horizon optimal control problems that appear in studies on economic growth processes, the properties of the adjoint variable in the relations of the Pontryagin maximum principle defined by a formula similar to the Cauchy formula for the solutions to linear differential systems are studied. It is shown that, under a dominating discount condition, the adjoint variable defined in this way satisfies both the core relations of the maximum principle (the adjoint system and the maximum condition) in the normal form and the additional stationarity condition for the Hamiltonian. In addition, a new economic interpretation of the adjoint variable based on this formula is considered.
Keywords:
optimal economic growth problems, infinite horizon, Pontryagin’s maximum principle, adjoint variable, stationarity condition for the Hamiltonian.
Citation:
S. M. Aseev, “On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 15–24; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 11–21
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\by S.~M.~Aseev
\paper On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 4
\pages 15--24
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 287
\issue , suppl. 1
\pages 11--21
\crossref{https://doi.org/10.1134/S0081543814090028}
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