A Projection-Type Method for Set Valued Variational Inequality Problems on Hadamard Manifolds

In this paper, we develop a projection-type algorithm for set-valued variational inequalities on Hadamard manifolds. The proposed method is well defined whether the solution set of the problem is non-empty or not. Under pseudomonotonicity assumptions on the underlying vector field, our method is convergent to a solution of the given set-valued variational inequality. The results presented in this paper generalize and improve some known results introduced by Tang et al. (Optimization 64(5):1081–1096, 2015).