Random-direction optimization algorithms with applications to threshold controls

This work develops a class of stochastic optimization algorithms. It aims t o provide numerical procedures for solving threshold-type optimal control p roblems. The main motivation stems from applications involving optimal or s uboptimal hedging policies, for example, production planning of manufacturi ng systems including random demand and stochastic machine capacity. The pro posed algorithm is a constrained stochastic approximation procedure that us es random-direction finite-difference gradient estimates. Under fairly gene ral conditions, the convergence of the algorithm is established and the rat e of convergence is also derived. A numerical example is reported to demons trate the performance of the algorithm.