Weak and strong convergence of a modified double inertial projection algorithm for solving variational inequality problems

We propose a new double inertial projection algorithm by combining the subgradient extragradient algorithm with the projection contraction algorithm. On one hand, our algorithm requires the mapping to be Lipschitz continuous, but without the Lipschitz constant. On the other hand, this algorithm only requires the mapping is quasimonotone.Under some mild conditions, we obtain a weak convergence result of the algorithm. In addition, we give a strong convergence result of the algorithm when the mapping is strongly pseudomonotone. Some numerical experiments are given to show the effectiveness of the proposed algorithm.