一类超线性收敛的广义拟Newton算法

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…

A CLASS OF GENERALIZED QUASINEWTON ALGORITHM WITH SUPER-LINEAR CONVERGENCE

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.