Abstract In this article, we study a class of pseudomonotone split variational inequality problems (VIPs) with non-Lipschitz operator. We propose new inertial extragradient method self-adaptive step sizes for finding the solution to aforementioned problem in framework Hilbert spaces. Moreover, prove strong convergence result proposed algorithm without prior knowledge operator norm and under mil...

Abstract For the purpose of this article, we introduce a modified form generalized system variational inclusions, called inclusion problems (GSMVIP). This problem reduces to classical and inequalities problems. Motivated by several recent results related subgradient extragradient method, propose new method for finding common element set solutions GSMVIP finite family Under suitable assumptions,...

Nonconvex–nonconcave saddle-point optimization in machine learning has triggered lots of research for studying non-monotone variational inequalities (VIs). In this work, we introduce two mirror frameworks, called extragradient method and extrapolation method, approximating solutions to relatively Lipschitz monotone-like VIs. The former covers the well-known Nemirovski’s prox Nesterov’s dual rec...