Accelerated subgradient extragradient methods with increasing self-adaptive step size for variational inequalities

The main purpose of this paper is to propose and analyze two accelerated subgradient extragradient methods with increasing self-adaptive step size for solving pseudomonotone variational inequality problems in Hilbert spaces. Under some appropriate conditions imposed on the parameters, we combine the inertial subgradient extragradient method with viscosity and Mann-type iterative methods, respectively, and obtain two new algorithms and their corresponding strong convergence theorems. Different from the classical subgradient extragradient method, we introduce new parameters to control the step size, which can effectively improve the convergence process. Finally, the performance of the proposed algorithms is compared with existing related algorithms through several numerical experiments.