Abstract

We present version IV of the stochastic optimization algorithm ALOPEX, together with an analytic proof of its convergence. The aim of the optimization is to find the (optimum) values of the control variables that maximize function f which describes the system under study. ALOPEX optimization methods are driven by the parallel incoherent dithering of the control variables and the time dependence of the feedback. Any possible local extrema are avoided by the introduction of noise. ALOPEX stochastic optimization has been proved to be a very powerful tool for the calculation of the optimal values of the control variables of dynamical systems in real time. The main advantage of the method is that no knowledge of the dynamics of the system or of the functional dependence of the cost function on the control variables, is required. Applications of ALOPEX IV stochastic optimization will also be presented, such as its successful implementation to the problem of finding the optimum fit of a dynamical systems model to the time series of raw physiological (heart rate) data.