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应用数学学报  1983, Vol. 6 Issue (3): 376-385    DOI:
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一个改进的超记忆梯度法的收敛性及其敛速估计
赵庆祯
曲阜师范学院
CONVERGENCE AND RATE OF CONVERGENCE OF AN IMPROVED SUPERMEMORY GRADIENT METHOD
Zhao Qing-zhen
Qufu Tethers' College
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摘要 问题:min{f(x)|x∈En},f(x)为实值函数; 记号:gj为f(x)在xj处的梯度列向量,x*为问题的最优解,H(x)、H*分别表示f(x)在x和x*处的Hessian矩阵,上标“,”表示矩阵的转置。给定实数序列{βj}、βj≥0、βj→0(j→∞),常数a>0,整数k1<n-1,整数p≥n及x的初始近似x0
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赵庆祯
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Abstract: This paper gives an improved supermemory gradient for the problem of minimizing a function without any restriction. The method (including the memory gradient method) is shown to be convergent. Moreover the rate of convergence is shown to be n-step superlinear, and n-step quadratic under some special conditions. With the supermemory gradient method, the requirement for multidimensional optimal search in the original algorithm is avoided. Hence it suffices to make one-dimensional optimal search in the algorithm.
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收稿日期: 1981-05-15;
引用本文:   
赵庆祯. 一个改进的超记忆梯度法的收敛性及其敛速估计[J]. 应用数学学报, 1983, 6(3): 376-385.
Zhao Qing-zhen. CONVERGENCE AND RATE OF CONVERGENCE OF AN IMPROVED SUPERMEMORY GRADIENT METHOD[J]. Acta Mathematicae Applicatae Sinica, 1983, 6(3): 376-385.
 
[1] A. Miele, J. W. Cantrell, Memory Gradient Method for the Minimization of Functions, J. Opt Theory&Applics, 3(1969), 459-470.
[2] M. A. Wolfe, A Quasi-Newton Method With Memory for Unconstrained Function Minimization, J Inst. Maths Applics, 15(1975), 85-94.
[3] M. A. Wolfe, C. Yiazmineky, Supermemory Descent Methods for Unconstrained Minimization. J Opt. Theory&Applics, 18(1976), 455-468.
[4] G. P. MeComick, K. Ritter, Alternative Proofs of the Convergeuce Properties of the Conjugate Gradient Method, J. Opt. Theory&Applics,13(1974), 497-518.
[5] E.E.Cragg, A. Y. Levy, Study on a Supermemory Gradient method for the Minimization of Functions, J. Opt. Theory&Applics, 4;3 (1969), 191-205.
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