无线性搜索下修正的共轭梯度法的收敛性

本文提出了一类修正共轭梯度法.该方法的特点是：（1）步长由一个固定的公式计算;（2）在无线性搜索的条件下,迭代方向是充分下降方向.在水平集有界和函数Lipschitz连续的条件下,方法具有全局收敛性.最后给出了初步的数值实验验证了方法的有效性.

The Convergence of a Modified Conjugate Gradient Method Without Line Search

In this paper,a class of modified conjugate gradient method is proposed.The method has the following attractive properties：（1） the step-size is determined by a formula;（2） the iterative direction is always a sufficiently descent direction without utilizing the line search.Under the boundedness of the level set and the Lipschitz continuity of the underlying function,the proposed methods is global convergent.Some numerical results are given to illustrate the effectiveness of the proposed methods.