ABSTRACT

In this paper, we are concerned with the problem of finding fixed points of nonexpansive mappings on Hadamard manifolds. To solving this kind of problem, a modified Riemannian Halpern algorithm, which is a natural generalization of a modified Halpern algorithm in Euclidean space is proposed. By giving some mild assumptions and necessary lemmas, the global convergence of the proposed algorithm is established. Finally, when the problem is solved in the framework of Hadamard manifolds, the numerical experiments show the effectiveness of the proposed algorithm, especially in computational time and number of iterations.

中文翻译：

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用于 Hadamard 流形上非膨胀映射的改进黎曼 Halpern 算法

摘要

在本文中，我们关注的是在 Hadamard 流形上寻找非膨胀映射的不动点的问题。为解决此类问题，提出了一种改进的黎曼Halpern算法，它是改进的Halpern算法在欧氏空间中的自然推广。通过给出一些温和的假设和必要的引理，建立了所提出算法的全局收敛性。最后，当问题在阿达玛流形的框架下求解时，数值实验表明了所提算法的有效性，尤其是在计算时间和迭代次数方面。