For controlled Markov processes taking values in a Polish space,
control problems with ergodic cost, infinite-horizon discounted cost and
finite-horizon cost are studied. Each is posed as a convex optimization problem
wherein one tries to minimize a linear functional on a closed convex set of
appropriately defined occupation measures for the problem. These are
characterized as solutions of a linear equation asssociated with the problem.
This characterization is used to establish the existence of optimal Markov
controls. The dual convex optimization problem is also studied.
Publié le : 1996-07-14
Classification:
Controlled Markov processes,
occupation measures,
optimal control,
infinite-dimensional linear programming,
93E20,
60J25
@article{1065725192,
author = {Bhatt, Abhay G. and Borkar, Vivek S.},
title = {Occupation measures for controlled Markov processes:
characterization and optimality},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1531-1562},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725192}
}
Bhatt, Abhay G.; Borkar, Vivek S. Occupation measures for controlled Markov processes:
characterization and optimality. Ann. Probab., Tome 24 (1996) no. 2, pp. 1531-1562. http://gdmltest.u-ga.fr/item/1065725192/