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一类超线性收敛的广义拟Newton算法
引用本文:焦宝聪. 一类超线性收敛的广义拟Newton算法[J]. 高等学校计算数学学报, 1999, 21(2): 178-188
作者姓名:焦宝聪
作者单位:首都师范大学数学系!北京100037
摘    要:1引言考虑无约束最优化问题其中目标函数f(x)二阶连续可微,记fk=f(x),当充分小时,有如下近似关系:它们对二次函数皆严格成立.考虑选代其中B(G的近似)已知,为某种线搜索确定的步长.对B修正产生B,即U为待定n阶矩阵.若要求B+满足关系即B满足拟Newton方程,由它可导出许多著名的拟Newton算法[1-[4]).若要求B满足关系则可导出伪Newton-δ族校正公式,它不再是Huang族成员[6].从信息资源的利用看,(1.6)仅利用了与信息,(1.7)仅利用了与信息.一般而言,较多的信…

关 键 词:超线性收敛 广义拟牛顿算法 无约束最优化

A CLASS OF GENERALIZED QUASINEWTON ALGORITHM WITH SUPER-LINEAR CONVERGENCE
Jiao Baocong. A CLASS OF GENERALIZED QUASINEWTON ALGORITHM WITH SUPER-LINEAR CONVERGENCE[J]. Numerical Mathematics A Journal of Chinese Universities, 1999, 21(2): 178-188
Authors:Jiao Baocong
Affiliation:Capital Normal University
Abstract:in this paper, we present a class of algorithms which are generalized quasi-Newton methods for unconstrained optimization. These methods do not belong to the Huang class. Comparing the new algorithms with quasi-Netwton methods, they do not increase computing capacity and can obtain more information. The sequence of matrix updated by the new algorithms are all symmetric and positive definite. When f(x) is uniform convex function, the global convergence and the super= linear convenience of these algorithms with wolfe inexact one search are proved.
Keywords:Unconstrained optimization   generalized quasi-Newton method   global convergence   superlinar convergence
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