A NEW DOUBLE INERTIAL SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING QUASIMONOTONE VARIATIONAL INEQUALITY PROBLEMS

In order to solve variational inequality problems for which the cost operator is quasimonotone and Lipschitz continuous in real Hilbert spaces, we propose a new double inertial subgradient extragradient method. The new method involves double inertial extrapolation steps and a self-adaptive step size. The weak convergence result of our method is established under some mild assumptions. The advantages of our method over many existing methods are illustrated via numerical experiments. Finally, we apply our results to an image restoration problem.