Abstract
We present the basic theorems for cost minimization and for DPs with an absorbing set of states. We also prove the basic theorem using reachable states. The important notion of a bounding function is introduced.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adomian, G., & Lee, E. S. (1986). The research contributions of Richard Bellman. Computers & Mathematics with Applications Series A, 12, 633–651.
Almudevar, A. (2014). Approximate iterative algorithms. Leiden: CRC Press/Balkema.
Bellman, R. (1957). Dynamic programming. Princeton: Princeton University Press.
Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Belmont: Athena Scientific.
Chang, H. S., Fu, M. C., Hu, J., & Marcus, S. I. (2007). Simulation-based algorithms for Markov decision processes. London: Springer.
Dreyfus, S. E., & Law, A. M. (1977). The art and theory of dynamic programming. New York: Academic Press.
Gani, J. (1984). Obituary: Richard Bellman. Journal of Applied Probability, 21, 935–936.
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.
Karlin, S. (1955). The structure of dynamic programming models. Naval Research Logistics Quarterly, 2, 285–294 (1956).
Lew, A. (1986). Richard Bellman’s contributions to computer science. Journal of Mathematical Analysis and Applications, 119, 90–96.
Morin, T. L. (1978). Computational advances in dynamic programming. In Dynamic programming and its applications (pp. 53–90). New York: Academic Press.
Porteus, E. L. (1975). An informal look at the principle of optimality. Management Science, 21, 1346–1348.
Powell, W. B. (2007). Approximate dynamic programming. New York: Wiley.
van Roy, B. (2002). Neuro-dynamic programming: Overview and recent trends. In E. Feinberg & Shwartz, A. (Eds.) Handbook of Markov decision processes: Methods and applications. Boston: Springer.
Sniedovich, M. (1992). Dynamic programming. New York: Marcel Dekker Inc.
Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning. Cambridge: The MIT Press.
Yakowitz, S. J. (1969). Mathematics of adaptive control processes. New York: American Elsevier Publishing Co., Inc.
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). Additional General Issues. In: Dynamic Optimization. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-48814-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-48814-1_3
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)