The minimization of a convex function defined over the grid Z/sup p/ is considered. A truncated fixed gain simultaneous perturbation stochastic approximation (SPSA) method is proposed and investigated in combination with devices borrowed from the Markov-chain Monte-Carlo literature. In particular, the performance of the proposed method is improved by choosing suitable acceptance probabilities. A new Markovian optimization problem is formulated to get the best rejection probability and gain. A simulation result is presented.