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

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.

Keywords:

• Variational inequalities
• monotone operator
• logarithmic-quadratic proximal method
• convergence rate
• projection method
• 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.

Additional information

Funding

M. H. Xu was partially supported by the NSFC [grant number 11471156].