# Average cost Markov control processes with weighted norms: value iteration

Evgueni Gordienko; Onésimo Hernández-Lerma

Applicationes Mathematicae (1995)

- Volume: 23, Issue: 2, page 219-237
- ISSN: 1233-7234

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topGordienko, Evgueni, and Hernández-Lerma, Onésimo. "Average cost Markov control processes with weighted norms: value iteration." Applicationes Mathematicae 23.2 (1995): 219-237. <http://eudml.org/doc/219127>.

@article{Gordienko1995,

abstract = {This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.},

author = {Gordienko, Evgueni, Hernández-Lerma, Onésimo},

journal = {Applicationes Mathematicae},

keywords = {average cost optimality equation; strong average optimality; (discrete-time) Markov control processes; long-run average cost; weighted norms; Markov control processes; convergence; value iteration; average cost optimality},

language = {eng},

number = {2},

pages = {219-237},

title = {Average cost Markov control processes with weighted norms: value iteration},

url = {http://eudml.org/doc/219127},

volume = {23},

year = {1995},

}

TY - JOUR

AU - Gordienko, Evgueni

AU - Hernández-Lerma, Onésimo

TI - Average cost Markov control processes with weighted norms: value iteration

JO - Applicationes Mathematicae

PY - 1995

VL - 23

IS - 2

SP - 219

EP - 237

AB - This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.

LA - eng

KW - average cost optimality equation; strong average optimality; (discrete-time) Markov control processes; long-run average cost; weighted norms; Markov control processes; convergence; value iteration; average cost optimality

UR - http://eudml.org/doc/219127

ER -

## References

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- [3] J. Flynn, On optimality criteria for dynamic programs with long finite horizons, J. Math. Anal. Appl. 76 (1980), 202-208. Zbl0438.90100
- [4] E. Gordienko and O. Hernández-Lerma, Average cost Markov control processes with weighted norms: existence of canonical policies, this volume, 199-218. Zbl0829.93067
- [5] O. Hernández-Lerma, Adaptive Markov Control Processes, Springer, New York, 1989.
- [6] O. Hernández-Lerma and J. B. Lasserre, A forecast horizon and a stopping rule for general Markov decision processes, J. Math. Anal. Appl. 132 (1988), 388-400. Zbl0646.90090
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- [8] O. Hernández-Lerma and J. B. Lasserre, Linear programming and average optimality of Markov control processes on Borel spaces-unbounded costs, SIAM J. Control Optim. 32 (1994), 480-500. Zbl0799.90120
- [9] O. Hernández-Lerma and J. B. Lasserre, Discrete-Time Markov Control Processes, book in preparation. Zbl0724.93087
- [10] G. P. Klimov, Existence of a final distribution for an irreducible Feller process with invariant measure, Math. Notes 37 (1985), 161-163. Zbl0659.60101
- [11] R. Montes-de-Oca and O. Hernández-Lerma, Value iteration in average cost Markov control processes on Borel spaces, Acta Appl. Math., to appear. Zbl0843.93093
- [12] E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators, Cambridge University Press, Cambridge, 1984. Zbl0551.60066
- [13] R. Rempała, Forecast horizon in a dynamic family of one-dimensional control problems, Dissertationes Math. 315 (1991). Zbl0754.90063
- [14] H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1971. Zbl0197.03501
- [15] M. Schäl, Conditions for optimality and for the limit of n-stage optimal policies to be optimal, Z. Wahrsch. Verw. Gebiete 32 (1975), 179-196. Zbl0316.90080
- [16] L. I. Sennott, Value iteration in countable state average cost Markov decision processes with unbounded costs, Ann. Oper. Res. 28 (1991), 261-272. Zbl0729.90088
- [17] D. J. White, Dynamic programming, Markov chains, and the method of successive approximations, J. Math. Anal. Appl. 6 (1963), 373-376. Zbl0124.36404

## Citations in EuDML Documents

top- Evgueni Gordienko, Onésimo Hernández-Lerma, Average cost Markov control processes with weighted norms: existence of canonical policies
- Evgueni I. Gordienko, Francisco Salem-Silva, Estimates of stability of Markov control processes with unbounded costs
- Evgueni I. Gordienko, J. Adolfo Minjárez-Sosa, Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion
- Raúl Montes-de-Oca, Francisco Salem-Silva, Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains
- Onésimo Hernández-Lerma, Oscar Vega-Amaya, Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality

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