一族共轭梯度法的全局收敛性

Global Convergence of a Family of Conjugate Gradient Methods

提出了求解无约束优化问题的一族共轭梯度法，这族方法包含Ｆｌｅｔｃｈｅｒ提出的共轭下降法。文中证明了一种非精确线性搜索条件能够保证这族方法的下降性和全局收敛性，其收敛结果与Ｄａｉ和Ｙｕａｎ１９９６年给出的关于共轭下降法的相一致。

AbstractIn this paper, a family of conjugate gradient methods for unconstrained optimization is proposed which includes the conjugate descent mehtod given by Fletcher R. It is proved that a kind of inexact linear search condition can nensure the descent property and the global converence of the family of methods, and the convergence result of it coincides with that of the conjugate descent method given by Dai and Yuan.