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Stability and characterisation conditions in negative programming

  • P. Whittle (a1)

Abstract

Let F be the infinite-horizon minimal cost function, and FK S the minimal cost function for horizon s and terminal cost function K. In Section 2 we define the ‘stable domain' (the set of K for which ), determine some of its properties, and relate these to the questions of stability of the process (whether ) and whether a given solution of the dynamic programming equation can be identified with F These ideas are developed in Sections 3 and 5 for various strengthenings and weakenings of the hypothesis of non-negative costs. In Section 5 we derive a new sufficient condition for stability and for characterisation of F.

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Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, U.K.

References

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Bertsekas, D. P. (1976) Dynamic Programming and Stochastic Control. Academic Press, New York.
Hinderer, K. (1970) Foundations of Non-Stationary Dynamic Programming with Discrete Time Parameter. Springer-Verlag, Berlin.
Whittle, P. (1979) A simple condition for regularity in negative programming. J. Appl. Prob. 16, 305318.

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Stability and characterisation conditions in negative programming

  • P. Whittle (a1)

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