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Russia Yekaterinburg
Section  Mathematics 
Title  Properties of the value function in optimal control problems with infinite horizon 
Author(s)  Bagno A.L.^{a}, Tarasyev A.M.^{b} 
Affiliations  Ural Federal University^{a}, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{b} 
Abstract  The article investigates properties of the value function of the optimal control problem on infinite horizon with an unlimited integrand index appearing in the quality functional with a discount factor. The estimate is derived for approximating the value function in a problem with the infinite horizon by levels of value functions in problems with lengthening finite horizons. The structure of the value function is identified basing on stationary value functions which depend only on phase variables. The description is given for the asymptotic growth of the value function generated by various types of the quality functional applied in economic and financial modeling: logarithmic, power, exponential, linear functions. The property of continuity is specified for the value function and estimates are deduced for the Hölder parameters of continuity. These estimates are needed for the development of grid algorithms designed for construction of the value function in optimal control problems with infinite horizon. 
Keywords  optimal control, infinite horizon, value function, estimation of continuity modulus, asymptotic properties 
UDC  517.977 
MSC  49K15 
DOI  10.20537/vm160101 
Received  27 October 2015 
Language  Russian 
Citation  Bagno A.L., Tarasyev A.M. Properties of the value function in optimal control problems with infinite horizon, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 314. 
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