Bounds on discrete dynamic programming recursions. I. Models with non-negative matrices

 Access to full text

 Full (PDF)

1. R. Bellman, On a Quasi-Linear Equation, Canad. J. Math. 8 (1956), 198-202. (1956) Zbl0071.34902MR0077782
2. R. Bellman, A Markovian Decision Process, J. Math. Mecb. 6 (1957), 670-684. (1957) Zbl0078.34101MR0091859
3. R. Bellman, Introduction to Matrix Analysis, McGraw Hill, New York 1960. Second edition 1970. (1960) Zbl0124.01001MR0258847
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. (1965) MR0176871
5. F. R. Gantmakher, Teoriya matric, Second edition. Nauka, Moscow 1966. (1966) 
6. R. A. Howard, Dynamic Programming and Markov Processes, Technology Press and Wiley Press, New York 1960. (1960) Zbl0091.16001MR0118514
7. R. A. Howard J. E. Matheson, Risk-sensitive Markov Decision Prccesses, Manag. Sci. 18 (1972), 7, 357-369. (1972) MR0292497
8. E. Lanery, Étude asymptotique des systèmes Markoviens à commande, Rev. Franc. Inf. Rech. Oper. 3 (1967), 1, 3-56. (1967) Zbl0159.48804MR0226950
9. 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
10. P. Mandl, Decomposable Non-Negative Matrices in a Dynamic Programming Problem, Czech. Math. J. 20 (1970), 3, 504-510. (1970) Zbl0209.22902MR0264978
11. A. M. Ostrowski, Solution of Equations and System of Equations, Academic Press, New York 1960. (1960) 
12. U. G. Rothblum, Algebraic Eigenspaces of Nonnegative Matrices, Linear Algebra Applic. 72 (1975), 281-292. (1975) Zbl0321.15010MR0404298
13. U. G. Rothblum, Multiplicative Markov Decision Chains, PhD Dissertation, Dept. Oper. Res., Stanford Calif. 1974. (1974) 
14. U. G. Rothblum, Normalized Markov Decision Chains II - Optimality of Nonstationary Policies, SIAM J. Control. Optim. 15 (1977), 2, 221-232. (1977) Zbl0367.90118MR0437085
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. (1977) MR0465243
16. K. Sladký, On Dynamic Programming Recursion for Multiplicative Markov Decision Chains, Math. Progr. Study 6 (1976), 216-226. (1976) MR0452725
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. (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. (1978) 
20. A. F. Veinott, Jr., Discrete Dynamic Programming with Sensitive Discount Optimality Criteria, Ann. Math. Stat. 40 (1969), 5,1635-1660. (1969) Zbl0183.49102MR0256712
21. W. H. M. Zijms, On Nonnegative Matrices in Dynamic Programming I, Memorandum Cosor 79-10, Eindhoven University of Technology, Eindhoven 1979. (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. (1979) 

1. Karel Sladký, Growth rates and average optimality in risk-sensitive Markov decision chains
2. Nico M. van Dijk, Karel Sladký, Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
3. Alfredo Alanís-Durán, Rolando Cavazos-Cadena, An optimality system for finite average Markov decision chains under risk-aversion
4. Karel Sladký, Bounds on discrete dynamic programming recursions. II. Polynomial bounds on problems with block-triangular structure
5. Karel Sladký, On the existence of stationary optimal policies in discrete dynamic programming
6. Raúl Montes-de-Oca, Elena Zaitseva, About stability of risk-seeking optimal stopping