@article {IOPORT.01160084,
    author       = {Hern\'andez-Lerma, On\'esimo and Lasserre, Jean B.},
    title        = {Linear programming approximations for Markov control processes in metric spaces.},
    year         = {1998},
    journal      = {Acta Applicandae Mathematicae},
    volume       = {51},
    number       = {2},
    issn         = {0167-8019},
    pages        = {123-139},
    publisher    = {Springer, Dordrecht},
    doi          = {10.1023/A:1005826226226},
    abstract     = {The authors develop linear programming techniques (LP) for discrete-time Markov control processes (MCP) in an uncountable metric space, particularly suitable for computational purposes. First, the authors introduce the associated LP equivalent to the MCP in the sense that $\rho^*=\min\bbfP$, where $\rho^*$ and $\min\bbfP$ are the optimum values of MCP and LP respectively [cf. the authors' book, Discrete-time Markov control processes: Basic optimality criteria (1995; Zbl 0840.93001)]. Then, using a suitable aggregation-relaxation procedure to approximate $\bbfP$ by LPs with a finite number of decision variables, it is shown that under mild assumptions these procedures converge to $\min \bbfP$. The basic difference between the schemes of the authors and those of other researchers is that the authors use approximations in weak (or weak*) topologies rather than in normed topologies.},
    reviewer     = {Wu Chengxun (Shanghai)},
    identifier   = {01160084},
}