Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices
Kybernetika (1980)
- Volume: 16, Issue: 6, page (526)-547
- ISSN: 0023-5954
Access Full Article
topHow to cite
topSladký, Karel. "Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices." Kybernetika 16.6 (1980): (526)-547. <http://eudml.org/doc/28460>.
@article{Sladký1980,
author = {Sladký, Karel},
journal = {Kybernetika},
keywords = {discrete dynamic programming; policy iteration algorithm; growth bounds},
language = {eng},
number = {6},
pages = {(526)-547},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices},
url = {http://eudml.org/doc/28460},
volume = {16},
year = {1980},
}
TY - JOUR
AU - Sladký, Karel
TI - Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices
JO - Kybernetika
PY - 1980
PB - Institute of Information Theory and Automation AS CR
VL - 16
IS - 6
SP - (526)
EP - 547
LA - eng
KW - discrete dynamic programming; policy iteration algorithm; growth bounds
UR - http://eudml.org/doc/28460
ER -
References
top- R. Bellman, On a Quasi-Linear Equation, Canad. J. Math. 8 (1956), 198-202. (1956) Zbl0071.34902MR0077782
- R. Bellman, A Markovian Decision Process, J. Math. Mecb. 6 (1957), 670-684. (1957) Zbl0078.34101MR0091859
- R. Bellman, Introduction to Matrix Analysis, McGraw Hill, New York 1960. Second edition 1970. (1960) Zbl0124.01001MR0258847
- B. W. Brown, On the Iterative Method of Dynamic Programming in a Finite Space Discrete Time Markov Processes, Ann. Math. Stat. 36 (1965), 4, 1279-1285. (1965) MR0176871
- F. R. Gantmakher, Teoriya matric, Second edition. Nauka, Moscow 1966. (1966)
- R. A. Howard, Dynamic Programming and Markov Processes, Technology Press and Wiley Press, New York 1960. (1960) Zbl0091.16001MR0118514
- R. A. Howard J. E. Matheson, Risk-sensitive Markov Decision Prccesses, Manag. Sci. 18 (1972), 7, 357-369. (1972) MR0292497
- E. Lanery, Étude asymptotique des systèmes Markoviens à commande, Rev. Franc. Inf. Rech. Oper. 3 (1967), 1, 3-56. (1967) Zbl0159.48804MR0226950
- P. Mandl E. Seneta, The Theory of Non-Negative Matrices in a Dynamic Programming Problem, Austral. J. Stat. 11 (1969), 2, 85-96. (1969) MR0411642
- P. Mandl, Decomposable Non-Negative Matrices in a Dynamic Programming Problem, Czech. Math. J. 20 (1970), 3, 504-510. (1970) Zbl0209.22902MR0264978
- A. M. Ostrowski, Solution of Equations and System of Equations, Academic Press, New York 1960. (1960)
- U. G. Rothblum, Algebraic Eigenspaces of Nonnegative Matrices, Linear Algebra Applic. 72 (1975), 281-292. (1975) Zbl0321.15010MR0404298
- U. G. Rothblum, Multiplicative Markov Decision Chains, PhD Dissertation, Dept. Oper. Res., Stanford Calif. 1974. (1974)
- U. G. Rothblum, Normalized Markov Decision Chains II - Optimality of Nonstationary Policies, SIAM J. Control. Optim. 15 (1977), 2, 221-232. (1977) Zbl0367.90118MR0437085
- P. J. Schweitzer A. Federgruen, The Asymptotic Behavior of Undiscounted Value Iteration in Markov Decision Problems, Mathem. Oper. Res. 2 (1977), 4, 360-381. (1977) MR0465243
- K. Sladký, On Dynamic Programming Recursion for Multiplicative Markov Decision Chains, Math. Progr. Study 6 (1976), 216-226. (1976) MR0452725
- K. Sladký, Successive Approximation Methods for Dynamic Programming Models, In: Proceedings of the Third Formator Symposium on the Analysis of Largs-Scale Systems. (L. Bakule, J. Beneš, eds.) Academia, Prague 1979. (1979)
- K. Sladký, Bounds on Discrete Dynamic Programming Recursions II - Polynomial Bounds on Problems with Block-Triangular Structure, Submitted to Kybernetika.
- K. Sladký, On Functional Equations of Discrete Dynamic Programming with Non-Negative Matrices, Research Report No. 900, Institute of Information Theory and Automation, Prague 1978. (1978)
- A. F. Veinott, Jr., Discrete Dynamic Programming with Sensitive Discount Optimality Criteria, Ann. Math. Stat. 40 (1969), 5,1635-1660. (1969) Zbl0183.49102MR0256712
- W. H. M. Zijms, On Nonnegative Matrices in Dynamic Programming I, Memorandum Cosor 79-10, Eindhoven University of Technology, Eindhoven 1979. (1979)
- W. H. M. Zijms, Maximizing the Growth of the Utility Vector in a Dynamic Programming Model, Memorandum Cosor 79-11, Eindhoven University of Technology, Eindhoven 1979. (1979)
Citations in EuDML Documents
top- Nico M. van Dijk, Karel Sladký, Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
- Karel Sladký, Growth rates and average optimality in risk-sensitive Markov decision chains
- Alfredo Alanís-Durán, Rolando Cavazos-Cadena, An optimality system for finite average Markov decision chains under risk-aversion
- Karel Sladký, Bounds on discrete dynamic programming recursions. II. Polynomial bounds on problems with block-triangular structure
- Karel Sladký, On the existence of stationary optimal policies in discrete dynamic programming
- Raúl Montes-de-Oca, Elena Zaitseva, About stability of risk-seeking optimal stopping
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.