Infinite-Horizon Deterministic Dynamic Programming in Discrete Time: A Monotone Convergence Principle and a Penalty Method

Takashi Kamihigashi and Masayuki Yao
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Masayuki Yao: Graduate School of Economics, Keio University

No DP2016-05, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: We consider infinite-horizon deterministic dynamic programming problems in discrete time. We show that the value function of such a problem is always a fixed point of a modi ed version of the Bellman operator. We also show that value iteration converges increasingly to the value function if the initial function is dominated by the value function, is mapped upward by the modified Bellman operator, and satisfies a transversality-like condition. These results require no assumption except for the general framework of infinite-horizon d-terministic dynamic programming. As an application, we show that the value function can be approximated by computing the value function of an unconstrained version of the problem with the constraint replaced by a penalty function.

Keywords: Dynamic programming; Bellman operator; Fixed point; Value iteration (search for similar items in EconPapers)
Pages: 17 pages
Date: 2016-02, Revised 2016-05
New Economics Papers: this item is included in nep-dge
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