Some self-adaptive inertial algorithms for solving variational inequalities over the solution set of the split variational inequality problem

Tóm tắt báo cáo

This paper investigates some new inertial self-adaptive iterative algorithms for solving variational inequalities over the solution set of the split variational inequality problem with multiple output sets in real Hilbert spaces. The strong convergence results are given under some mild conditions that are widely used in the convergence analysis.  The inertial technique accelerates our algorithms and eliminates the dependence on the norm of the transformation operators and the strongly monotone and Lipschitz continuous constants of the involved operator. Two applications in the network bandwidth allocation problem and the image classification problem are shown, and some numerical experiments are presented to show the advantages of the proposed algorithm.