Nonautonomous stochastic search for global minimum in continuous optimization

Various iterative stochastic optimization schemes can be represented as discrete-time Markov processes defined by the nonautonomous equation Xt+1=Tt(Xt,Yt)Xt+1=Tt(Xt,Yt), where YtYt is an independent sequence and TtTt is a sequence of mappings. This paper presents a general framework for the study of the stability and convergence of such optimization processes. Some applications are given: the mathematical convergence analysis of two optimization methods, the elitist evolution strategy (μ+λ)(μ+λ) and the grenade explosion method, is presented.