STOCHASTIC COMPARISON ALGORITHM FOR CONTINUOUS OPTIMIZATION WITH ESTIMATION

The problem of stochastic optimization for arbitrary objective functio ns presents a dual challenge. First, one needs to repeatedly estimate the objective function; when no closed-form expression is available, t his is only possible through simulation. Second, one has to face the p ossibility of determining local, rather than global, optima. In this p aper, we show how the stochastic comparison approach recently proposed in Ref. 1 for discrete optimization can be used in continuous optimiz ation. We prove that the continuous stochastic comparison algorithm co nverges to an epsilon-neighborhood of the global optimum for any epsil on>0. Several applications of this approach to problems with different features are provided and compared to simulated annealing and gradien t descent algorithms.