Self-adaptive inertial subgradient extragradient algorithm for solving pseudomonotone variational inequalities

In this paper, we introduce an inertial algorithm for solving classical variational inequalities with Lipschitz continuous and pseudomonotone mapping in real Hilbert space. The algorithm is inspired by subgradient extragradient method and the inertial method with a new step size. The convergence of algorithm is established without the knowledge of the Lipschitz constant of the mapping. Finally, some numerical experiments are presented to show the efficiency and advantage of the proposed algorithm.

Automated summary

This paper introduces an inertial algorithm for solving classical variational inequalities in real Hilbert space with Lipschitz continuous and pseudomonotone mapping. The algorithm, inspired by subgradient extragradient method and inertial method, utilizes a new step size. Convergence is established without knowledge of the Lipschitz constant of the mapping, and numerical experiments demonstrate the efficiency and advantage of the proposed algorithm.