A new alternating direction method for solving variational inequalities

We introduce a modified alternating direction method for structured monotone variational inequalities by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. This method only needs functional values for given variables in the solution process and avoids the task of estimating the co-coercive modulus. All the computing process are easily implemented and the global convergence is also presented under mild assumptions. Some preliminary computational results are given.