Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices
Kybernetika, Tome 16 (1980) no. 6, pp. 526-547 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 90C39
@article{KYB_1980_16_6_a3,
     author = {Sladk\'y, Karel},
     title = {Bounds on discrete dynamic programming recursions. {I.} {Models} with non-negative matrices},
     journal = {Kybernetika},
     pages = {526--547},
     year = {1980},
     volume = {16},
     number = {6},
     mrnumber = {607292},
     zbl = {0454.90085},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1980_16_6_a3/}
}
TY  - JOUR
AU  - Sladký, Karel
TI  - Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices
JO  - Kybernetika
PY  - 1980
SP  - 526
EP  - 547
VL  - 16
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_1980_16_6_a3/
LA  - en
ID  - KYB_1980_16_6_a3
ER  - 
%0 Journal Article
%A Sladký, Karel
%T Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices
%J Kybernetika
%D 1980
%P 526-547
%V 16
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_1980_16_6_a3/
%G en
%F KYB_1980_16_6_a3
Sladký, Karel. Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices. Kybernetika, Tome 16 (1980) no. 6, pp. 526-547. http://geodesic.mathdoc.fr/item/KYB_1980_16_6_a3/

[1] R. Bellman: On a Quasi-Linear Equation. Canad. J. Math. 8 (1956), 198-202. | MR | Zbl

[2] R. Bellman: A Markovian Decision Process. J. Math. Mecb. 6 (1957), 670-684. | MR | Zbl

[3] R. Bellman: Introduction to Matrix Analysis. McGraw Hill, New York 1960. Second edition 1970. | MR | Zbl

[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

[5] F. R. Gantmakher: Teoriya matric. Second edition. Nauka, Moscow 1966.

[6] R. A. Howard: Dynamic Programming and Markov Processes. Technology Press and Wiley Press, New York 1960. | MR | Zbl

[7] R. A. Howard J. E. Matheson: Risk-sensitive Markov Decision Prccesses. Manag. Sci. 18 (1972), 7, 357-369. | MR

[8] E. Lanery: Étude asymptotique des systèmes Markoviens à commande. Rev. Franc. Inf. Rech. Oper. 3 (1967), 1, 3-56. | MR | Zbl

[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

[10] P. Mandl: Decomposable Non-Negative Matrices in a Dynamic Programming Problem. Czech. Math. J. 20 (1970), 3, 504-510. | MR | Zbl

[11] A. M. Ostrowski: Solution of Equations and System of Equations. Academic Press, New York 1960.

[12] U. G. Rothblum: Algebraic Eigenspaces of Nonnegative Matrices. Linear Algebra Applic. 72 (1975), 281-292. | MR | Zbl

[13] U. G. Rothblum: Multiplicative Markov Decision Chains. PhD Dissertation, Dept. Oper. Res., Stanford Calif. 1974.

[14] U. G. Rothblum: Normalized Markov Decision Chains II - Optimality of Nonstationary Policies. SIAM J. Control. Optim. 15 (1977), 2, 221-232. | MR | Zbl

[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

[16] K. Sladký: On Dynamic Programming Recursion for Multiplicative Markov Decision Chains. Math. Progr. Study 6 (1976), 216-226. | MR

[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.

[18] K. Sladký: Bounds on Discrete Dynamic Programming Recursions II - Polynomial Bounds on Problems with Block-Triangular Structure. Submitted to Kybernetika.

[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.

[20] A. F. Veinott, Jr.: Discrete Dynamic Programming with Sensitive Discount Optimality Criteria. Ann. Math. Stat. 40 (1969), 5,1635-1660. | MR | Zbl

[21] W. H. M. Zijms: On Nonnegative Matrices in Dynamic Programming I. Memorandum Cosor 79-10, Eindhoven University of Technology, Eindhoven 1979.

[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.