Adaptive optimization with constraints: Convergence and oscillatory behaviour

Abstract

The problem of adaptive minimization of globally unknown functionals under constraints on the independent variable is considered in a stochastic framework. The CAM algorithm for vector problems is proposed. By resorting to the ODE analysis for analysing stochastic algorithms and singular perturbation methods, it is shown that the only possible convergence points are the constrained local minima. Simulation results in 2 dimensions illustrate this result. © Springer-Verlag Berlin Heidelberg 2005.