A descent alternating direction method for monotone variational inequalities with separable structure

To solve a special class of variational inequalities with separable structure, this paper proposes a descent alternating direction method based on a new residual function. The most prominent characteristic of the method is that it is easily performed, in which, only some orthogonal projections and function evaluations are involved at each iteration, so its computational load is very tiny. Under mild conditions, the global convergence of the proposed descent method is proved.