Modified accelerated algorithms for solving variational inequalities

In this paper, we propose two inertial algorithms with new stepsize rule for solving a monotone and Lipschitz variational inequality in a Hilbert space and prove some weak and strong convergence theorems of the proposed inertial algorithms. The algorithms use variable stepsizes which are updated at each iteration by a simple computation without any linesearch. A new stepsize rule presented in the paper has allowed the algorithms to work without the prior knowledge of Lipschitz constant of operator. Finally, we give several numerical results to demonstrate the computational performance of the new algorithms in comparison with other algorithms.