An inertial Popov extragradient projection algorithm for solving multi-valued variational inequality problems

In this paper, we present an inertial Popov extragradient projection algorithm for solving multi-valued variational inequality problems in finite-dimensional Euclidean space. The global convergence of this algorithm is proved whenever the underlying mapping is Lipschitz continuous and pseudomonotone on the feasible set. Numerical experiments show that new algorithm is more efficient than algorithm of Ye [An improved projection method for solving generalized variational inequality problems. Optimization. 2018;67:1-11] whenever the underlying mapping is Lipschitz continuous. Here inertial technique can accelerate extragradient algorithm although the underlying mapping is multi-valued.