伪Newton－R族算法的导出及其性质

Derivation and Property of Algorithm of Pseudo-Newton-R Class

对无约束优化问题提出了一个新的拟Ｎｅｗｔｏｎ法（伪Ｎｅｗｔｏｎ－Ｒ族算法），这种方法具有二次终止性及调比不变性。它产生的近似Ｈｅｓｓｅ阵序列保持正定对称传递性。该算法对一致凸函数具有全局收敛性和超线性收敛性。

In this paper,a new quasi-Newton method (algorithm of pseudo-Newton-R class) is presented for unconstrained optimization,this method possesses the property of finite convergence for quadratic function and scale invariance.The sequence of matrices updated by the method maintains positive definite symmetric transitivity.This method is global and superlinear convergent for the uniform convex function.