Fixed Point Methods and Optimization

Electronic ISSN: 3008-1548

DOI: 10.69829/fpmo

Double inertial steps relaxed projection algorithm for pseudomonotone variational inequalities

Fixed Point Methods and Optimization, Volume 3, Issue 1, April 2026, Pages 20–35

JIAYI ZOU

School of Mathematical Science, China West Normal University, Nanchong, 637009, P.R. China

MINGLU YE

Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications, School of Mathematical Science, China West Normal University, Nanchong, 637009, P.R. China


Abstract

In this paper, we propose an outer approximation algorithm for solving pseudomonotone variational inequalities (VI) in Hilbert space. The algorithm incorporates a double inertial technique, resulting in the double inertial relaxed projection algorithm (DIRPA). DIRPA generalizes the algorithm proposed by Yao, Iyiola and Shehu [J Sci Comput, 2022, 90(71): 1-29] (YIS Alg for short). Unlike the YIS Alg, DIRPA allows both inertial step-sizes to be adaptively updated. By taking suitable parameters, the global weak convergence of DIRPA is established under the same assumptions with YIS Alg. Numerical experiments show the efficiency of DIRPA.


Cite this Article as

Jiayi Zou and Minglu Ye, Double inertial steps relaxed projection algorithm for pseudomonotone variational inequalities, Fixed Point Methods and Optimization, 3(1), 20–35, 2026