New descent LQP alternating direction methods for solving a class of structured variational inequalities

In this paper, we propose two descent alternating direction methods based on a logarithmic-quadratic proximal method for structured variational inequalities. The first method can be viewed as an extension of the method proposed by Bnouhachem and Xu (Comput. Math. Appl. 67:671-680, 2014) by performing an additional step at each iteration. The second method generates the new iterate by searching the optimal step size along a new descent direction, which can be viewed as a refinement and improvement of the first one. Under certain conditions, the global convergence of the both methods is proved.