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

Karel Sladký

Kybernetika (1980)

  • Volume: 16, Issue: 6, page (526)-547
  • ISSN: 0023-5954

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Sladký, 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

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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. (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) 

Citations in EuDML Documents

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  1. Nico M. van Dijk, Karel Sladký, Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
  2. Karel Sladký, Growth rates and average optimality in risk-sensitive Markov decision chains
  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

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