一种基于弱拟牛顿方程的单调梯度法的收敛性

摘要

基于弱拟牛顿方程,Leong W J等人提出了一种单调梯度法,该算法在每次迭代时利用对角矩阵逼近Hessian矩阵,使计算量和存储量明显减少,并且此算法对凸函数具有收敛性。在此算法的基础上,进一步研究了算法对于一般函数的收敛性,并证明了在一定的假设条件下算法仍具有全局收敛性、R-线性收敛性和超线性收敛性。%Based on weak Quasi-Newton equation,a monotone gradient algorithm was proposed by Leong W J et al.Hessian matrix was approximated by diagonal matrix in this method,thus reducing the computation and storing space.The convergence of the method has been proved when it was applied to the minimization of the convex function.On the basis of this algorithm,we can study the convergence of the algorithm for the minimization of the general function.The global convergence,the R-linear convergence and the superlinear convergence of the algorithm have been proved under given conditions.