Abstract

The aim of this article is to introduce new iterative algorithms for finding a common solution from the set of equilibrium points of an equilibrium problem and of singularities of an inclusion problem on Hadamard manifolds. We discuss some particular cases of the problem with the proposed algorithms. The convergence results of a sequence generated by the proposed algorithms are proved under mild assumptions on a Hadamard manifold. Moreover, we apply our results to solve optimization problems and variational inequality problems.

中文翻译：

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Hadamard流形上平衡问题和包含问题的分裂算法

摘要

本文的目的是介绍新的迭代算法，用于从平衡问题的平衡点集合和 Hadamard 流形上的包含问题的奇异点集合中找到公共解。我们使用所提出的算法讨论问题的一些特殊情况。在Hadamard流形上的温和假设下证明了由所提出算法生成的序列的收敛结果。此外，我们将我们的结果应用于解决优化问题和变分不等式问题。