| Abstract: | In this paper, we extend a projection-type method for variational inequalities from Euclidean spaces to Hadamard manifolds. The proposed method has the following nice features: (i) the algorithm is well defined whether the solution set of the problem is non-empty or not, under weak assumptions; (ii) if the solution set is non-empty, then the sequence generated by the method is convergent to the solution, which is closest to the initial point; and (iii) the existence of the solutions to variational inequalities can be verified through the behaviour of the generated sequence. The results presented in this paper generalize and improve some known results given in literatures. |
