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Identities relating forward and backward treatments of optimisation

Published online by Cambridge University Press:  14 July 2016

P. Whittle
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Abstract

A general form of Green's theorem is used to derive relations between expected costs for an optimisation problem and the distribution of state variable. A characterisation of the optimal stopping set and an alternative proof of the Howard improvement lemma emerge as non-trivial consequences.

Keywords

MARKOV DECISION PROCESSESDUALITYGREEN'S THEOREM
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 395 - 399
Copyright
Copyright © 1982 Applied Probability Trust 

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References

Blackwell, D. (1965) Discounted dynamic programming. Ann. Math. Statist. 36, 226–235.CrossRefGoogle Scholar
Derman, C. (1970) Finite State Markovian Decision Processes. Academic Press, New York.Google Scholar
Margenau, H. and Murphy, G. M. (1943) The Mathematics of Physics and Chemistry. Van Nostrand, New York.Google Scholar
Reid, D. W. and Teo, H. L. (1980) Optimal parameter selection for parabolic systems. Math. Operat. Res. 5, 467–479.CrossRefGoogle Scholar
Whittle, P. (1975) An approximate characterisation of optimal stopping boundaries. J. Appl. Prob. 10, 158–165.CrossRefGoogle Scholar
Whittle, P. (1982) Optimisation Over Time. Wiley Interscience, New York.Google Scholar