| Title:
|
Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices (English) |
| Author:
|
Sladký, Karel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
16 |
| Issue:
|
6 |
| Year:
|
1980 |
| Pages:
|
(526)-547 |
| . |
| Category:
|
math |
| . |
| MSC:
|
90C39 |
| idZBL:
|
Zbl 0454.90085 |
| idMR:
|
MR607292 |
| . |
| Date available:
|
2009-09-24T17:17:36Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125305 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/124353 |
| . |
| Reference:
|
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| Reference:
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[2] R. Bellman: A Markovian Decision Process.J. Math. Mecb. 6 (1957), 670-684. Zbl 0078.34101, MR 0091859 |
| Reference:
|
[3] R. Bellman: Introduction to Matrix Analysis.McGraw Hill, New York 1960. Second edition 1970. Zbl 0124.01001, MR 0258847 |
| Reference:
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[4] 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. MR 0176871 |
| Reference:
|
[5] F. R. Gantmakher: Teoriya matric.Second edition. Nauka, Moscow 1966. |
| Reference:
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[6] R. A. Howard: Dynamic Programming and Markov Processes.Technology Press and Wiley Press, New York 1960. Zbl 0091.16001, MR 0118514 |
| Reference:
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[7] R. A. Howard J. E. Matheson: Risk-sensitive Markov Decision Prccesses.Manag. Sci. 18 (1972), 7, 357-369. MR 0292497 |
| Reference:
|
[8] E. Lanery: Étude asymptotique des systèmes Markoviens à commande.Rev. Franc. Inf. Rech. Oper. 3 (1967), 1, 3-56. Zbl 0159.48804, MR 0226950 |
| Reference:
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[9] P. Mandl E. Seneta: The Theory of Non-Negative Matrices in a Dynamic Programming Problem.Austral. J. Stat. 11 (1969), 2, 85-96. MR 0411642 |
| Reference:
|
[10] P. Mandl: Decomposable Non-Negative Matrices in a Dynamic Programming Problem.Czech. Math. J. 20 (1970), 3, 504-510. Zbl 0209.22902, MR 0264978 |
| Reference:
|
[11] A. M. Ostrowski: Solution of Equations and System of Equations.Academic Press, New York 1960. |
| Reference:
|
[12] U. G. Rothblum: Algebraic Eigenspaces of Nonnegative Matrices.Linear Algebra Applic. 72 (1975), 281-292. Zbl 0321.15010, MR 0404298 |
| Reference:
|
[13] U. G. Rothblum: Multiplicative Markov Decision Chains.PhD Dissertation, Dept. Oper. Res., Stanford Calif. 1974. |
| Reference:
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[14] U. G. Rothblum: Normalized Markov Decision Chains II - Optimality of Nonstationary Policies.SIAM J. Control. Optim. 15 (1977), 2, 221-232. Zbl 0367.90118, MR 0437085 |
| Reference:
|
[15] P. J. Schweitzer A. Federgruen: The Asymptotic Behavior of Undiscounted Value Iteration in Markov Decision Problems.Mathem. Oper. Res. 2 (1977), 4, 360-381. MR 0465243 |
| Reference:
|
[16] K. Sladký: On Dynamic Programming Recursion for Multiplicative Markov Decision Chains.Math. Progr. Study 6 (1976), 216-226. MR 0452725 |
| Reference:
|
[17] 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. |
| Reference:
|
[18] K. Sladký: Bounds on Discrete Dynamic Programming Recursions II - Polynomial Bounds on Problems with Block-Triangular Structure.Submitted to Kybernetika. |
| Reference:
|
[19] 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. |
| Reference:
|
[20] A. F. Veinott, Jr.: Discrete Dynamic Programming with Sensitive Discount Optimality Criteria.Ann. Math. Stat. 40 (1969), 5,1635-1660. Zbl 0183.49102, MR 0256712 |
| Reference:
|
[21] W. H. M. Zijms: On Nonnegative Matrices in Dynamic Programming I.Memorandum Cosor 79-10, Eindhoven University of Technology, Eindhoven 1979. |
| Reference:
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[22] 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. |
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