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

In this paper, we propose a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The predictor is obtained by solving series of related systems of nonlinear equations, and the new iterate is obtained by a convex combination of the previous point and the one generated by a projection-type method along a new descent direction. Global convergence of the new method is proved under certain assumptions. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method.Qatar University Start-Up Grant: QUSG-CAS-DMSP-13/14-8.Scopu

An alternating direction method for solving convex nonlinear semidefinite programming problems

An alternating direction method is proposed for solving convex semidefinite optimization problems. This method only computes several metric projections at each iteration. Convergence analysis is presented and numerical experiments in solving matrix completion problems are reported