R-linear convergence analysis of two golden ratio projection algorithms for strongly pseudo-monotone variational inequalities

In this paper, we combine the golden ratio method with the projection algorithm to obtain the golden ratio projection algorithm. In order to get better convergence speed, we also propose an alternating golden ratio projection algorithm. Unlike ordinary inertial extrapolation, golden ratio method is constructed based on a convex combined structure about the entire iterative trajectory. The advantages of the proposed algorithms require only one projection onto the feasible set and do not require knowledge of the Lipschitz constant for the operator since our algorithms use self-adaptive step-sizes. The R-linear convergence results of the two algorithms are established for strongly pseudo-monotone variational inequality. Finally, we present some numerical experiments to show the efficiency and advantages of the proposed algorithms.