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Integral functionals, normal integrands and measurable selections
- Publisher
- INFORMS
- Copyright
- Copyright © INFORMS
- Subject
- Research Article
- ISSN
- 0364-765X
- eISSN
- 1526-5471
- DOI
- 10.1287/moor.5.2.308
- Publisher site
- See Article on Publisher Site
Abstract
The optimality equation of discrete time dynamic programming is considered when state space and action space are finite dimensional Euclidean spaces. Based on a measurable selection theorem we give an elementary derivation of sufficient conditions to assure that the optimal value operator behaves well. For our model these conditions are weaker than those described in the existing literature. Under related conditions it is easy to prove that an optimal Markovian strategy exists for a finite stage Markovian stochastic optimization problem, and that the optimal strategies are completely characterized by the minimum sets of the optimality equations. This is illustrated with a general N-stage inventory control model.
Journal
Mathematics of Operations Research – INFORMS
Published: May 1, 1980
Keywords: Keywords : Markovian dynamic programming ; measurable selection ; normal integrand ; N -stage inventory model ; existence of an optimal strategy