Article ID: | iaor201522432 |
Volume: | 35 |
Issue: | 5 |
Start Page Number: | 575 |
End Page Number: | 591 |
Publication Date: | Sep 2014 |
Journal: | Optimal Control Applications and Methods |
Authors: | Gonzlez-Hernndez Juan, Lpez-Martnez Raquiel R, Minjrez-Sosa J Adolfo, Gabriel-Arguelles J Rigoberto |
Keywords: | optimization, markov processes, programming: linear |
In this paper, we study constrained Markov control processes on Borel spaces with possibly unbounded one‐stage cost, under a discounted optimality criterion with random discount factor and restrictions of the same kind. We prove that the corresponding optimal control problem is equivalent to an infinite‐dimensional linear programming problem. In addition, considering the dual program, we show that there is no duality gap, and moreover, the strong duality condition holds. Hence, both programs are solvable, and their optimal values coincide.