Approximating infinite horizon stochastic optimal control in discrete time with constraints

Traditional approaches to solving stochastic optimal control problems involve dynamic programming, and solving certain optimality equations. When recast as stochastic programming problems, structural aspects such as convexity are retained, and numerical solution procedures based on decomposition and duality may be exploited. This paper explores a class of stationary, infinite-horizon stochastic optimization problems with discounted cost criterion. Constraints on both states and controls are permitted, and modeled in the objective function by allowing it to take infinite values. Approximating techniques are developed using variational analysis, and intuitive lower bounds are obtained via averaging the future. These bounds could be used in a finite-time horizon stochastic programming setting to find solutions numerically. Research supported in part by a grant of the National Science Foundation. AMS Classification 46N10, 49N15, 65K10, 90C15, 90C46