This article aims to introduce and analyze the viscosity method for hierarchical variational inequalities involving a ϕ-contraction mapping defined over a common solution set of variational inclusion and fixed points of a nonexpansive mapping on Hadamard manifolds. Several consequences of the composed method and its convergence theorem are presented. The convergence results of this article generalize and extend some existing results from Hilbert/Banach spaces and from Hadamard manifolds. We also present an application to a nonsmooth optimization problem. Finally, we clarify the convergence analysis of the proposed method by some computational numerical experiments in Hadamard manifold.

中文翻译：

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Hadamard流形上的分层变分不等式和变分包含的粘度方法

本文旨在介绍和分析用于层次变分不等式的粘性方法，该方法涉及在一般的解集和Hadamard流形上的非扩张映射的不动点集的共同解集上定义的ϕ收缩映射。提出了组合方法及其收敛定理的几个结果。本文的收敛性结果对Hilbert / Banach空间和Hadamard流形的一些现有结果进行了概括和扩展。我们还提出了一个解决非平稳优化问题的应用程序。最后，通过Hadamard流形中的一些计算数值实验，阐明了该方法的收敛性分析。