no. 2
Solving MDP functional equations by lexicographic optimization
RAIRO - Operations Research - Recherche Opérationnelle, Tome 16 (1982) no. 2, pp. 91-98. 
@article{RO_1982__16_2_91_0,
     author = {Schweitzer, Paul J.},
     title = {Solving {MDP} functional equations by lexicographic optimization},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {91--98},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {2},
     year = {1982},
     mrnumber = {679631},
     zbl = {0485.90085},
     language = {en},
     url = {http://www.numdam.org/item/RO_1982__16_2_91_0/}
}
TY  - JOUR
AU  - Schweitzer, Paul J.
TI  - Solving MDP functional equations by lexicographic optimization
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 1982
SP  - 91
EP  - 98
VL  - 16
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/RO_1982__16_2_91_0/
LA  - en
ID  - RO_1982__16_2_91_0
ER  - 
%0 Journal Article
%A Schweitzer, Paul J.
%T Solving MDP functional equations by lexicographic optimization
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 1982
%P 91-98
%V 16
%N 2
%I EDP-Sciences
%U http://www.numdam.org/item/RO_1982__16_2_91_0/
%G en
%F RO_1982__16_2_91_0
Schweitzer, Paul J. Solving MDP functional equations by lexicographic optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 16 (1982) no. 2, pp. 91-98. http://www.numdam.org/item/RO_1982__16_2_91_0/

1. R. G. Bartle, The Elements of Real Analysis, Wiley, New York, second edition, 1976. | MR | Zbl

2. R. Bellman, Functional Equations in the Theory of Dynamic Programming V. Positivity and Quasi-Linearity, Proc. Nat. Acad. Sc. U.S.A., Vol. 41, 1955, pp. 743-746. | MR | Zbl

3. I. Brosh, E. Shlifer and P. Schweitzer, Generalized Markovian Decision Processes, Zeitschrift fur Operations Research, Vol. 21, 1977, pp. 173-186. | MR | Zbl

4. E. Denardo, Contraction Mappings in the Theory Underlying Dynamic Programming, S.I.A.M. Rev., Vol. 9, 1967, pp. 165-177. | MR | Zbl

5. E. Denardo and B. Fox, Multichain Markov Renewal Programs, S.I.A.M. J. Appl. Math., Vol. 16, 1968, pp. 468-487. | MR | Zbl

6. E. V. Denardo, Computing a Bias-optimal Policy in a Discrete-time Markov Decision Problem, Oper. Res., Vol. 18, 1970, pp. 279-289. | MR | Zbl

7. E. V. Denardo, Markov Renewal Programs with Small Interest Rates, Ann. Math. Statist., Vol. 42, 1971, pp. 477-496. | MR | Zbl

8. A. Federgruen and P. J. Schweitzer, A Fixed Point Approach to Undiscounted Markov Renewal Programs, Working Paper 8024, Graduate School of ManagementUniversity of Rochester, Rochester, New York, 1980; Also Columbia University, Graduate School of Business Working Paper 351 A, 1980 (Revised 1981). | Zbl

9. R. C. Grinold, A Generalized Discrete Dynamic Programming Model, Management Science, Vol. 20, 1974, pp. 1092-1103. | MR | Zbl

10. R. A. Howard, Dynamic Programming and Markov Processes, Wiley, New York, 1960. | MR | Zbl

11. W. Jewell, Markov Renewal Programming, Operations Research, Vol. 11, 1963, pp. 938-971. | MR | Zbl

12. J. L. Kelley, General Topology, Van Nostrand, Princeton, New Jersey, 1955. | MR | Zbl

13. G. J. Koehler, A. B. Whinston and G. P. Wright, Optimization Over Leontief Substitution Systems, North-Holland, Amsterdam, 1975. | MR | Zbl

14. B. L. Miller and A. F. Veinott Jr., Discrete Dynamic Programming with a Small Interest Rate, Ann. Math. Statist., Vol. 40, 1969, 366-370. | MR | Zbl

15. S. M. Ross, Applied Probability Models with Optimization Applications, Holden-Day, San Francisco, 1970. | MR | Zbl

16. P. Schweitzer, Perturbation Theory and Finite Markov Chains, J. Appl. Prob., Vol. 5, 1968, pp. 401-413. | MR | Zbl

17. P. J. Schweitzer and B. Gavish, An Optimality Principle for Markovian Decision Processes, J. Math. Anal. and Appl. Vol. 54, 1976, pp. 173-184. | MR | Zbl

18. S. S. Sheu and K.-J. Farn, Sufficient Condition for the Existence of a Stationary 1- Optimal Plan in Compact Action Markovian Decision Processes, Recent Developments in Markov Decision Processes, R. HARTLEY, L. C. THOMAS, D. J.WHITE, Eds., Academic Press, New York, 1980, pp. 111-126.

19. A. F. Jr. Veinott, On Finding Optimal Policies in Discrete Dynamic Programming with No Discounting, Ann. Math. Statist., Vol. 37, 1966, pp. 1284-1294. | MR | Zbl

20. A. F. Jr. Veinott, Discrete Dynamic Programming with Sensitive Discount Optimality Criteria, Ann. Math. Statist., Vol. 40, 1969, pp. 1635-1660. | MR | Zbl