In this paper, we propose the DFP algorithm with inexact line search for unconstrained optimization problems on Riemannian manifolds. Under some reasonable conditions, the global convergence result is established and the superlinear local convergence rate of the DFP algorithm is proved on Riemannian manifolds. The preliminary computational experiment is also reported to illustrate the effectiveness of the DFP algorithm.

中文翻译：

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黎曼流形无约束优化问题DFP算法的收敛性分析

在本文中，我们针对黎曼流形上的无约束优化问题提出了不精确线搜索的 DFP 算法。在一定合理条件下，建立了全局收敛结果，并在黎曼流形上证明了DFP算法的超线性局部收敛速度。还报告了初步的计算实验，以说明 DFP 算法的有效性。