Two-step inertial Tseng's extragradient method for variational inequality and hierarchical fixed-point problems
Abstract
We developed novel inertial Tseng-type extragradient methods, in both two-step and one-step formulations based on the Krasnosel'skiǐ-Mann iteration framework. The proposed schemes were designed to solve variational inequality problems (VIPs) and hierarchical fixed-point problems (HFPPs) governed by nonexpansive and quasi-nonexpansive operators in Hilbert spaces. The obtained sequences were shown to converge weakly to a shared solution, together with additional supporting results, and its applicability was demonstrated through an example. This formulation generalizes and brings together several known methods and outcomes in the literature.
Fields of Study & Subjects
Optimization and Variational Analysis
Contact Mechanics and Variational Inequalities
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 7
- Pages
- 19567–19592
- Publication date
- 1 January 2026