带非精确线搜索的调整搜索方向DFP算法(英文)

The Revised DFP Algorithm Without Exact Line Search

本文介绍一类新的带调整搜索方向的Broyden算法.我们着重讨论带调整搜索方向的DFP算法的收敛性,在某些非精确线搜索的情况下,我们证明对连续可微目标函数,这算法是整体收敛的,而对一致凸目标函数,收敛速度是一步超线收敛的.从这篇文章的证明过程中,可以得到对一致凸目标函数,DFP算法具有一步超线形收敛.

In this paper we proposed a new class of the Broyden algorithms with revised search direction. In practical, we discuss the convergence of the DFP algorithms with revised search direction. Under some inexact line searches, we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of the algorithm is one-step superlinear.