Abstract
In many special models the existence of maximizers at all stages (and hence by the OC in Theorem 2.3.3(c) also of s-optimal action sequences for all initial states s) can be established by ad hoc methods. The existence of a maximizer at each stage is also obvious if the set D(s) of admissible actions is finite for all s. In Proposition 7.1.10 we gave a result which covers many applications where S and A are intervals. The existence problem for maximizers under more general conditions is most easily dealt with under assumptions which are so strong that continuity (or at least upper semicontinuity) of W n and also of V n is implied.
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References
Bertsekas, D. P., & Shreve, S. E. (1978). Stochastic optimal control. New York: Academic Press.
Dubins, L. E., & Savage, L. J. (1965). How to gamble if you must. Inequalities for stochastic processes. New York: McGraw-Hill.
Dynkin, E. B., & Yushkevich, A. A. (1979). Controlled Markov processes. Berlin: Springer.
Hinderer, K. (1970). Foundations of non-stationary dynamic programming with discrete time parameter (Lecture Notes in Operations Research and Mathematical Systems, Vol. 33). Berlin: Springer.
Schäl, M. (1975). Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32, 179–196.
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Hinderer, K., Rieder, U., Stieglitz, M. (2016). Existence of Optimal Action Sequences. In: Dynamic Optimization. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-48814-1_9
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DOI: https://doi.org/10.1007/978-3-319-48814-1_9
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