Hilbert 空间中关于分层变分不等式问题与不动点问题的投影算法

Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (1): 94-107.

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Projection Algorithm for Hierarchical Variational Inequality Problem and Fixed Point Problem in Hilbert Space

Jiayu Liu(), Xinghui Gao^*(), Luhan Dan

College of Mathematics and Computer Science, Yan'an University, Shaanxi Yan'an 716000

Received:2025-03-10 Revised:2025-06-29 Online:2026-02-26 Published:2026-01-19
Contact: Xinghui Gao E-mail:3438956880@qq.com;yadxgaoxinghui@163.com
Supported by:
NSFC(61866038);Shaanxi Special Support Plan for High-level Talent Program (2021)

Abstract

Abstract:

This paper introduces a novel multi-step inertial regularization algorithm in Hilbert spaces, designed to solve the common solution of hierarchical variational inequality problems and quasi-non expansive mapping fixed-point problems. Under certain conditions, the strong convergence theorem for this iterative sequence generated by the algorithm is established. Finally, a numerical example is provided to demonstrate that this algorithm is more efficient than the existing ones.

Key words: hierarchical variational inequalities, multi-step inertial regularization algorithm, strong convergence theorem

CLC Number:

O177.91

Jiayu Liu, Xinghui Gao, Luhan Dan. Projection Algorithm for Hierarchical Variational Inequality Problem and Fixed Point Problem in Hilbert Space[J].Acta mathematica scientia,Series A, 2026, 46(1): 94-107.

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References 19

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Projection Algorithm for Hierarchical Variational Inequality Problem and Fixed Point Problem in Hilbert Space

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