Gradient Average, While Perturbation Algorithm Analysis

According to stoachstic systemic characteristic ,In this paper , we define simultaneous perturbation stochastic approximation method with gradient averaging. Then, resorting to method of the Lyapunov fuanction ,we give the sufficient and necessary conditions of the convergence of this algorithm. In addition, we discuss some properties of this algorithm.In this paper ,resorting to the Lyapunov function,we study the convergence of this algorithm.According to the characteristic of the stochastic system , we define simultaneous perturbation stochastic approximation method with gradient averaging. Then ,we discuss the sufficient and necessary conditions of convengence . we obtain the theorm 3.1At last,we discuss the asymptotic normality and asymptotic efficiency. Besides hypothesis the gradient function is locally Lipschitz continual and the once differential matrix of the gradient function is stable under some conditions, we hypothesis the noise sequences is a fuanctuon sequnence about a martingale sequence.then we obtain the theorm 4.1...