A descent LQP alternating direction method for solving variational inequality problems with separable structure

Based on the logarithmic-quadratic proximal method, a descent alternating direction method is introduced for structured variational inequalities in the paper. The proposal method generates the new iteration by searching the optimal step size along the integrated descent direction from two descent directions. Global convergence of the proposal method is proved under certain assumptions. To illustrate the proposal method and demonstrate its efficiency, some applications and their numerical results are also provided.