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 X t + 1 = T t ( X t , Y t ) , where Y t is an independent sequence and T t 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 ) and the grenade explosion method, is presented.