论文标题
Riemannian Levenberg-Marquardt方法具有全球和本地收敛性能
Riemannian Levenberg-Marquardt Method with Global and Local Convergence Properties
论文作者
论文摘要
我们将欧几里得空间上的levenberg-marquardt方法扩展到里曼尼亚歧管。尽管Peeters在1993年生产了Riemannian Levenberg-Marquardt（RLM）方法，但据我们所知，尚无对全球和局部收敛性质的理论保证进行分析。与Euclidean LM方法一样，如何更新称为阻尼参数的特定参数对其性能具有重大影响。我们提出了一种类似信任区域的方法来确定参数。我们评估了达到epsilon安置点的最坏情况迭代的复杂性，并证明其在局部误差结合条件下具有理想的局部收敛性。最后，我们通过数值实验证明了我们提出的算法的效率。
We extend the Levenberg-Marquardt method on Euclidean spaces to Riemannian manifolds. Although a Riemannian Levenberg-Marquardt (RLM) method was produced by Peeters in 1993, to the best of our knowledge, there has been no analysis of theoretical guarantees for global and local convergence properties. As with the Euclidean LM method, how to update a specific parameter known as the damping parameter has significant effects on its performances. We propose a trust-region-like approach for determining the parameter. We evaluate the worst-case iteration complexity to reach an epsilon-stationary point, and also prove that it has desirable local convergence properties under the local error-bound condition. Finally, we demonstrate the efficiency of our proposed algorithm by numerical experiments.
