On the principle of optimality for nonstationary deterministic dynamic programming

Takashi Kamihigashi

International Journal of Economic Theory, 2008, vol. 4, issue 4, 519-525

Abstract: This note considers a general nonstationary infinite‐horizon optimization problem in discrete time. We allow the state space in each period to be an arbitrary set, and the return function in each period to be unbounded. We do not require discounting, nor do we require the constraint correspondence in each period to be nonempty‐valued. The objective function is defined as the limit superior or inferior of the finite sums of return functions. We show that the sequence of time‐indexed value functions satisfies the Bellman equation if and only if its right‐hand side is well defined; that is, it does not involve −∞+ ∞.

Date: 2008
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https://doi.org/10.1111/j.1742-7363.2008.00092.x

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Working Paper: On the Principle of Optimality for Nonstationary Deterministic Dynamic Programming (2007)
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