Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102286
Title: On Hamiltonian as Limiting Gradient in Infinite Horizon Problem
Authors: Khlopin, D.
Issue Date: 2017
Publisher: Springer New York LLC
Citation: Khlopin D. On Hamiltonian as Limiting Gradient in Infinite Horizon Problem / D. Khlopin. — DOI 10.1007/s10883-016-9311-1 // Journal of Dynamical and Control Systems. — 2017. — Vol. 23. — Iss. 1. — P. 71-88.
Abstract: Necessary conditions of optimality in the form of the Pontryagin maximum principle are derived for the Bolza-type discounted problem with free right end. The optimality is understood in the sense of the uniformly overtaking optimality. Such process is assumed to exist, and the corresponding payoff of the optimal process (expressed in the form of improper integral) is assumed to converge in the Riemann sense. No other assumptions on the asymptotic behaviour of trajectories or adjoint variables are required. In this paper, we prove that there exists a corresponding limiting solution of the Pontryagin maximum principle that satisfies the Michel transversality condition; in particular, the stationarity condition of the maximized Hamiltonian and the fact that the maximized Hamiltonian vanishes at infinity are proved. The connection of this condition with the limiting subdifferentials of payoff function along the optimal process at infinity is showed. The case of payoff without discount multiplier is also considered. © 2016, Springer Science+Business Media New York.
Keywords: INFINITE HORIZON PROBLEM
LIMITING SUBDIFFERENTIAL
MICHEL CONDITION
PONTRYAGIN MAXIMUM PRINCIPLE
SHADOW PRICES
TRANSVERSALITY CONDITION FOR INFINITY
UNIFORMLY OVERTAKING OPTIMAL CONTROL
MAXIMUM PRINCIPLE
INFINITE HORIZON PROBLEMS
MICHEL CONDITION
OPTIMAL CONTROLS
SHADOW PRICE
SUBDIFFERENTIALS
TRANSVERSALITY CONDITIONS
HAMILTONIANS
URI: http://hdl.handle.net/10995/102286
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84959165669
PURE ID: 1380805
cb73f965-b8ee-4bd5-a173-e3edc544c144
ISSN: 10792724
DOI: 10.1007/s10883-016-9311-1
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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