OPTIMIZATION ALGORITHM WITH PROBABILISTIC ESTIMATION

In this paper, we present a stochastic optimization algorithm based on the idea of the gradient method which incorporates a new adaptive-pre cision technique. Because of this new technique, unlike recent methods , the proposed algorithm adaptively selects the precision without any need for prior knowledge on the speed of convergence of the generated sequence. With this new technique, the algorithm can avoid increasing the estimation precision unnecessarily, yet it retains its favorable c onvergence properties. In fact, it tries to maintain a nice balance be tween the requirements for computational accuracy and those for comput ational expediency. Furthermore, we present two types of convergence r esults delineating under what assumptions what kinds of convergence ca n be obtained for the proposed algorithm.