An alternated inertial proximal-type subgradient extragradient method for pseudo-monotone variational inequalities
Applicable Nonlinear Analysis, Volume 3, Issue 2, August 2026, Pages: 76–92
XU YU JIANG
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, China
GUI HUA SONG
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, China
MONIRUL ISLAM
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
ZAI YUN PENG
School of Mathematics, Yunnan Normal University, Kunming, China
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, China
Abstract
This paper proposes an alternated inertial proximal-type subgradient extragradient projection algorithm for solving pseudo-monotone variational inequality problems in real Hilbert spaces. We introduce an additional parameter in the second projection step to regulate the proximal-type update, which improves stability and accelerates convergence. Weak convergence of the generated sequence is established. Numerical experiments demonstrate that the proposed method outperforms several existing algorithms.
Cite this Article as
Xu Yu Jiang, Gui Hua Song, Monirul Islam, and Zai Yun Peng, An alternated inertial proximal-type subgradient extragradient method for pseudo-monotone variational inequalities, Applicable Nonlinear Analysis, 3(2), 76–92, 2026