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A new LQP alternating direction method for solving variational inequality problems with separable structure |
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| Authors: | Abdellah Bnouhachem Abdelouahed Hamdi M H Xu |
| Institution: | 1. School of Management Science and Engineering, Nanjing University, Nanjing, P.R. China.;2. ENSA, Ibn Zohr University, Agadir, Morocco.a.bnouhachem@uiz.ac.ma;4. Department of Mathematics, Statistics and Physics College of Arts and Sciences Qatar University, Doha, Qatar.;5. School of Mathematics and Physics, Changzhou University, Changzhou, P.R. China. |
| 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 |