Stochastic approximation for function minimization under quantization error

The simultaneous perturbation stochastic approximation (SPSA) method developed by Spall (1992) is applied and analyzed for function minimization under quantization error. It is proved that under certain conditions the estimator sequence converges with rate O(n/sup -/spl beta//2/) for some /spl beta/>0, where the rate is measured by the L/sub q/-norm of the estimation error for any 1/spl les/q