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Problems of Mathematical Control Theory
April 10, 2015 15:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)

Adjoint variables and intertemporal prices in optimal control problems with infinite time horizon

S. M. Aseev

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Abstract: Optimal control problems with infinite time horizon arise naturally in studies of processes of economic growth. The infinite time horizon may cause the appearance of various pathological phenomena in the relations of the corresponding general version of the Pontryagin maximum principle. In particular, the standard transversality conditions at infinity may fail. The goal of the talk is to present new versions of the maximum principle which contain an alternative characterization of the adjoint variable via formula similar to the Cauchy formula for solutions of linear differential systems.
We start with a variant of the maximum principle developed recently in the joint paper with V.M. Veliov. Then we present two new versions of the maximum principle which are formulated in terms of intertemporal prices and conditional value of the capital respectively. A few illustrative examples will be given.
1. 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, № 4 (2013), pp. 15–24. 2. 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, № 3 (2014), pp. 41–57.

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