On the principle of optimality for nonstationary deterministic dynamic programming
AbstractThis note studies 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, and do not 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, i.e., it does not involve -â+â.
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Bibliographic InfoArticle provided by The International Society for Economic Theory in its journal International Journal of Economic Theory.
Volume (Year): 4 (2008)
Issue (Month): 4 ()
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Other versions of this item:
- Takashi Kamihigashi, 2007. "On the Principle of Optimality for Nonstationary Deterministic Dynamic Programming," Discussion Paper Series 200, Research Institute for Economics & Business Administration, Kobe University.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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