Linear Programming Approximations for Markov Control Processes in Metric Spaces*

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We develop a general framework to analyze the convergence of linear-programming approximations for Markov control processes in metric spaces. The approximations are based on aggregation and relaxation of constraints, as well as inner approximations of the decision variables. In particular, conditions are given under which the control problem's optimal value can be approximated by a sequence of finite-dimensional linear programs.

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