建立在割线条件上的新Liu-Storey型共轭梯度法的全局收敛性(英文)

Global Convergence of New Liu-Storey Conjugate Gradient Methods Based on the Secant Condition

我们基于拟牛顿法的割线条件提出两种LS型共轭梯度法.有趣的是,我们提出的方法中对于βk的计算公式与戴和廖[3]提出的有相似的结构.但是,新方法能够在合理的假设下保证充分下降性,这一点是戴-廖方法所不具备的.在强Wolfe线搜索下,给出了新方法的全局收敛结果.数值结果论证了该方法的有效性.

In this paper, two new LS methods are proposed based on the secant condition of quasi- Newton methods. Interestingly,the formulas for flk in our methods have similar forms as those pro- posed by DAI and LIAO But superior to the DAI-LIAO method, the sufficient descent property of the proposed methods can be guaranteed under reasonable assumptions. Global convergence re- suits for the proposed methods with the strong Wolfe line search are established. Numerical results show that the new method is very efficient.