ABSTRACT
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.
Acknowledgments
The authors would like to thank the Associate Editor and anonymous referees for their valuable comments and suggestions which help us in improving the original version of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.