Geodesic
An unbounded Berge's minimum theorem with applications to discounted Markov decision processes
Kybernetika, Tome 48 (2012) no. 2, pp. 268-286

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

This paper deals with a certain class of unbounded optimization problems. The optimization problems taken into account depend on a parameter. Firstly, there are established conditions which permit to guarantee the continuity with respect to the parameter of the minimum of the optimization problems under consideration, and the upper semicontinuity of the multifunction which applies each parameter into its set of minimizers. Besides, with the additional condition of uniqueness of the minimizer, its continuity is given. Some examples of nonconvex optimization problems that satisfy the conditions of the article are supplied. Secondly, the theory developed is applied to discounted Markov decision processes with unbounded cost functions and with possibly noncompact actions sets in order to obtain continuous optimal policies. This part of the paper is illustrated with two examples of the controlled Lindley's random walk. One of these examples has nonconstant action sets.
Classification : 90A16, 90C40, 93E20
Keywords: Berge's minimum theorem; moment function; discounted Markov decision process; uniqueness of the optimal policy; continuous optimal policy 
@article{KYB_2012__48_2_a6,
     author = {Montes-de-Oca, Ra\'ul and Lemus-Rodr{\'\i}guez, Enrique},
     title = {An unbounded {Berge's} minimum theorem with applications to discounted {Markov} decision processes},
     journal = {Kybernetika},
     pages = {268--286},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2012},
     mrnumber = {2954325},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a6/}
}
TY  - JOUR
AU  - Montes-de-Oca, Raúl
AU  - Lemus-Rodríguez, Enrique
TI  - An unbounded Berge's minimum theorem with applications to discounted Markov decision processes
JO  - Kybernetika
PY  - 2012
SP  - 268
EP  - 286
VL  - 48
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a6/
LA  - en
ID  - KYB_2012__48_2_a6
ER  - 
%0 Journal Article
%A Montes-de-Oca, Raúl
%A Lemus-Rodríguez, Enrique
%T An unbounded Berge's minimum theorem with applications to discounted Markov decision processes
%J Kybernetika
%D 2012
%P 268-286
%V 48
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a6/
%G en
%F KYB_2012__48_2_a6
Montes-de-Oca, Raúl; Lemus-Rodríguez, Enrique. An unbounded Berge's minimum theorem with applications to discounted Markov decision processes. Kybernetika, Tome 48 (2012) no. 2, pp. 268-286. http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a6/