Abstract
We presented a new logarithmic-quadratic proximal alternating direction scheme for the separable constrained convex programming problem. The predictor is obtained by solving series of related systems of non-linear equations in a parallel wise. The new iterate is obtained by searching the optimal step size along a new descent direction. The new direction is obtained by the linear combination of two descent directions. Global convergence of the proposed method is proved under certain assumptions. We show the O(1 / t) convergence rate for the parallel LQP alternating direction method.
Acknowledgements
The authors are very grateful to the referees for their careful reading, comments and suggestions, which helped us improve the presentation of this paper.
Notes
No potential conflict of interest was reported by the authors.