A new extragradient-type method for mixed variational inequalities

In this paper, a new projection method for mixed variational inequalities is introduced in Euclidean spaces. The Armijo-type linesearch is similar to that of He’s method for variational inequalities. Under some suitable assumptions, we prove that the sequence generated by the proposed method is globally convergent to a solution of the problem. If, in addition, a certain error bound holds, we analyze the convergence rate of the iterative sequence. The results presented in this paper generalize and improve some known results given in literatures.