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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-48814-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48813-4
Online ISBN: 978-3-319-48814-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)