Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality

Onésimo Hernández-Lerma; Oscar Vega-Amaya

Applicationes Mathematicae (1998)

  • Volume: 25, Issue: 2, page 153-178
  • ISSN: 1233-7234

Abstract

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We consider discrete-time Markov control processes on Borel spaces and infinite-horizon undiscounted cost criteria which are sensitive to the growth rate of finite-horizon costs. These criteria include, at one extreme, the grossly underselective average cost

How to cite

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Hernández-Lerma, Onésimo, and Vega-Amaya, Oscar. "Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality." Applicationes Mathematicae 25.2 (1998): 153-178. <http://eudml.org/doc/219198>.

@article{Hernández1998,
abstract = {We consider discrete-time Markov control processes on Borel spaces and infinite-horizon undiscounted cost criteria which are sensitive to the growth rate of finite-horizon costs. These criteria include, at one extreme, the grossly underselective average cost},
author = {Hernández-Lerma, Onésimo, Vega-Amaya, Oscar},
journal = {Applicationes Mathematicae},
keywords = {uniform ergodicity; Lyapunov stability conditions; (discrete-time) Markov control processes; Poisson's equation; undiscounted cost criteria; existence; discrete-time Markov control processes; infinite horizon undiscounted cost criteria},
language = {eng},
number = {2},
pages = {153-178},
title = {Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality},
url = {http://eudml.org/doc/219198},
volume = {25},
year = {1998},
}

TY - JOUR
AU - Hernández-Lerma, Onésimo
AU - Vega-Amaya, Oscar
TI - Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality
JO - Applicationes Mathematicae
PY - 1998
VL - 25
IS - 2
SP - 153
EP - 178
AB - We consider discrete-time Markov control processes on Borel spaces and infinite-horizon undiscounted cost criteria which are sensitive to the growth rate of finite-horizon costs. These criteria include, at one extreme, the grossly underselective average cost
LA - eng
KW - uniform ergodicity; Lyapunov stability conditions; (discrete-time) Markov control processes; Poisson's equation; undiscounted cost criteria; existence; discrete-time Markov control processes; infinite horizon undiscounted cost criteria
UR - http://eudml.org/doc/219198
ER -

References

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  1. A. Arapostathis, V. S. Borkar, E. Fernández-Gaucherand, M. K. Ghosh and S. I. Marcus (1993), Discrete-time controlled Markov processes with average cost criterion: a survey, SIAM J. Control Optim. 31, 282-344. Zbl0770.93064
  2. R. Bellman (1957), A markovian decision process,z J. Math. Mech. 6, 679-684. Zbl0078.34101
  3. D. P. Bertsekas and S. E. Shreve (1978), Stochastic Optimal Control: The Discrete Time Case, Academic Press, New York. Zbl0471.93002
  4. B. W. Brown (1965), On the iterative method of dynamic programming on a finite space discrete time Markov process, Ann. Math. Statist. 33, 719-726. 
  5. D. A. Carlson, A. Haurie and A. Leizarowitz (1991), Infinite Horizon Optimal Control: Deterministic and Stochastic Systems, Springer, New York. Zbl0758.49001
  6. E. V. Denardo and U. G. Rothblum (1979), Overtaking optimality for Markov decision chains, Math. Oper. Res. 4, 144-152. Zbl0409.90084
  7. P. K. Dutta (1991), What do discounted optima converge to? A theory of discount rate asymptotics in economic models, J. Econom. Theory 55, 64-94. Zbl0743.90024
  8. E. B. Dynkin and A. A. Yushkevich (1979), Controlled Markov Processes, Springer, New York. Zbl0073.34801
  9. A. Ephremides and S. Verdú (1989), Control and optimization methods in communication network problems, IEEE Trans. Automat. Control 34, 930-942. Zbl0709.94667
  10. E. Fernández-Gaucherand, M. K. Ghosh and S. I. Marcus (1994), Controlled Markov processes on the infinite planning horizon: weighted and overtaking criteria, Z. Oper. Res. 39, 131-155. Zbl0809.90128
  11. J. Flynn (1980), On optimality criteria for dynamic programs with long finite horizons, J. Math. Anal. Appl. 76, 202-208. Zbl0438.90100
  12. D. Gale (1967), On optimal development in a multi-sector economy, Rev. Econom. Stud. 34, 1-19. P. W. Glynn and S. P. Meyn (1996), A Lyapunov bound for solutions of Poisson's equation, Ann. Probab. 24, 916-931. 
  13. E. Gordienko and O. Hernández-Lerma (1995a), Average cost Markov control processes with weighted norms: existence of canonical policies, Appl. Math. (Warsaw) 23, 199-218. Zbl0829.93067
  14. E. Gordienko and O. Hernández-Lerma (1995b), Average cost Markov control processes with weighted norms: value iteration, ibid., 219-237. Zbl0829.93068
  15. O. Hernández-Lerma (1989), Adaptive Markov Control Processes, Springer, New York. Zbl0698.90053
  16. O. Hernández-Lerma, J. C. Hennet and J. B. Lasserre (1991), Average cost Markov decision processes: optimality conditions, J. Math. Anal. Appl. 158, 396-406. Zbl0739.90072
  17. O. Hernández-Lerma and J. B. Lasserre (1996), Discrete-Time Markov Control Processes: Basic Optimality Criteria, Springer, New York. Zbl0840.93001
  18. O. Hernández-Lerma and J. B. Lasserre (1997), Policy iteration for average cost Markov control processes on Borel spaces, Acta Appl. Math. 47, 125-154. Zbl0872.93080
  19. O. Hernández-Lerma, R. Montes-de-Oca and R. Cavazos-Cadena (1991), Recurrence conditions for Markov decision processes with Borel state space: a survey, Ann. Oper. Res. 28, 29-46. Zbl0717.90087
  20. O. Hernández-Lerma and M. Muñoz de Ozak (1992), Discrete-time Markov control processes with discounted unbounded cost: optimality criteria, Kybernetika (Prague) 28, 191-212. Zbl0771.93054
  21. C. J. Himmelberg, T. Parthasarathy and F. S. Van Vleck (1976), Optimal plans for dynamic programming problems, Math. Oper. Res. 1, 390-394. Zbl0368.90134
  22. A. Leizarowitz (1988), Controlled diffusion processes on infinite horizon with the overtaking criterion, Appl. Math. Optim. 17, 61-78. Zbl0637.60055
  23. P. Mandl and M. Lausmanová (1991), Two extensions of asymptotic methods in controlled Markov chains, Ann. Oper. Res. 28, 67-79. Zbl0754.60081
  24. S. P. Meyn (1995), The policy improvement algorithm for Markov decision processes with general state space, preprint, Coordinated Science Laboratory, Univ. of Illinois, Urbana, Ill. 
  25. S. P. Meyn and R. L. Tweedie (1993), Markov Chains and Stochastic Stability, Springer, London. Zbl0925.60001
  26. R. Montes-de-Oca and O. Hernández-Lerma (1996), Value iteration in average cost Markov control processes on Borel spaces, Acta Appl. Math. 42, 203-222. Zbl0843.93093
  27. A. S. Nowak (1992), Stationary overtaking optimal strategies in Markov decision processes with general state space, preprint, Institute of Mathematics, Technical Univ. of Wrocław. 
  28. E. Nummelin (1984), General Irreducible Markov Chains and Non-Negative Operators, Cambridge Univ. Press, Cambridge. Zbl0551.60066
  29. S. Orey (1971), Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities, Van Nostrand Reinhold, London. Zbl0295.60054
  30. M. L. Puterman (1994), Markov Decision Processes, Wiley, New York. Zbl0829.90134
  31. F. P. Ramsey (1928), A mathematical theory of savings, Econom. J. 38, 543-559. 
  32. U. Rieder (1978), Measurable selection theorems for optimization problems, Manuscripta Math. 24, 115-131. Zbl0385.28005
  33. P. J. Schweitzer (1985), On undiscounted Markovian decision processes with compact action spaces, RAIRO Rech. Opér. 19, 71-86. Zbl0571.90095
  34. S. Stidham and R. Weber (1993), A survey of Markov decision models for control of networks of queues, Queueing Systems Theory Appl. 13, 291-314. Zbl0772.90082
  35. O. Vega-Amaya (1996), Overtaking optimality for a class of production-inventory systems, preprint, Departamento de Matemáticas, Universidad de Sonora. 
  36. A. F. Veinott, Jr. (1966), On finding optimal policies in discrete dynamic programming with no discounting, Ann. Math. Statist. 37, 1284-1294. Zbl0149.16301
  37. C. C. von Weizsäcker (1965), Existence of optimal programs of accumulation for an infinite horizon, Rev. Econom. Stud. 32, 85-104. 
  38. A. A. Yushkevich (1973), On a class of strategies in general Markov decision models, Theory Probab. Appl. 18, 777-779. Zbl0311.90081

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