一类广义拟牛顿算法的收敛性分析

Convergence Properties of A Class of Generalized Quasi-Newton Methods

根据提出的一种广义拟牛顿方程,推导出了一族广义拟牛顿校正公式,并给出了相应的广义拟牛顿算法。该算法具有很强的广泛性,它不仅包含了Zhang和焦宝聪提出的算法,还使得著名的B royden族成为它的一种特殊形式。实例证明:新的广义拟牛顿算法在一致凸的条件下具有整体收敛性和局部超线收敛性。

This paper presents a class of new generalized quasi - Newton methods for unconstrained optimization. The new methods are very extensive, including the methods proposed by Jiao and Zhang as well as the family of Broyden. The global convergence and the superlinear convergence of the new methods are also proved under the assumption of a uniform convex objective function.