APPROXIMATION OF INFINITE-DIMENSIONAL LINEAR-PROGRAMMING PROBLEMS WHICH ARISE IN STOCHASTIC-CONTROL

We study a general approximation scheme for infinite-dimensional linea r programming (LP) problems which arise naturally in stochastic contro l. We prove that the optimal value of the approximating problems conve rges to the value of the original LP problem. For the controls, we sho w that if the approximating optimal controls converge, the limiting co ntrol is an optimal control for the original LP problem. As an applica tion of this theory, we present numerical approximations to the LP for mulation of stochastic control problems in continuous time. We study l ong-term average and discounted control problems. For the example for which the theoretical solution is known, our approximation results are very accurate.