We study the convergence of a modified proximal point method for DC functions in Hadamard manifolds. We use the iteration computed by the proximal point method for DC function extended to the Riemannian context by Souza and Oliveira (J Glob Optim 63:797–810, 2015) to define a descent direction which improves the convergence of the method. Our method also accelerates the classical proximal point method for convex functions. We illustrate our results with some numerical experiments.

中文翻译：

---

Hadamard流形上的DC函数的一种改进的近点法

我们研究了Hadamard流形中DC函数的改进近点方法的收敛性。我们使用由Souza和Oliveira扩展到Riemann上下文的DC函数的近点方法计算出的迭代（J Glob Optim 63：797–810，2015）来定义下降方向，以改善该方法的收敛性。我们的方法还加速了凸函数的经典近点方法。我们通过一些数值实验来说明我们的结果。