共轭下降法的一个全局收敛性结果

A global convergence result for conjugate descent method

共轭梯度法是求解无约束最优化问题的一个著名方法 ,共轭下降法是其中的一种 ,它最早由 Fletcher提出 .在对共轭下降法进行研究并确定了步长λk时 ,使用了一种新的 Armijo类型的搜索 ,证明了新算法的可行性及全局收敛性 .提出的搜索简单易行 。

Conjugate gradient methods are well known for solving the unconstrained optimization problem. One of the conjugate gradient method is the conjugate descent (CD) method, which was introduced by Fletcher. In this paper, a new Armijo type line search is proposed, which is well defined and can ensure the global convergence of the conjugate descent method. The new line search is simple and easy to implement, which enriches the context of conjugate gradient methods.