DOI: 10.24193/fpt-ro.2025.2.20

Authors: Shenghua Wang, Yitong Shi and Rongguang Lin

Abstract: Hybrid steepest descent methods are used to solve a variational inequality problem (VIP) over the fixed point set of (quasi) nonexpansive mapping in the literature. In these results, the mapping involved in VIP is required to be Lipschitz continuous and strongly monotone. In this paper, we propose a new projection algorithm for solving a pseudomonotone VIP over the fixed point set of a quasi-nonexpansive mapping in Hilbert spaces. Compared the previous methods, the mapping is not assumed to be Lipschitz continuous, strongly monotone or uniformly continuous in our algorithm. We prove the weak convergence and estimate the convergence rate of the proposed algorithm. Some numerical examples are given to illustrate the effectiveness of our algorithm and compare the computed results with other related algorithms.

Key Words and Phrases: Pseudomonotone variational inequality, weak convergence, projection method, convergence rate.

2010 Mathematics Subject Classification: 65J15, 68W10, 47H09, 47H10.

Published on-line: May 1st, 2025.

Fulltext pdf

Back to volume's table of contents