A new LQP alternating direction method for solving variational inequality problems with separable structure. (1st December 2016)

• Record Type: Journal Article
• Authors: Bnouhachem, Abdellah; Hamdi, Abdelouahed; Xu, M. H.
• Is Part Of: Optimization. Volume 65:Number 12(2016)
• Page Start: 2251
• Page End: 2267
• Publication Date: 2016-12-01
• Subjects: Variational inequalities -- monotone operator -- logarithmic-quadratic proximal method -- convergence rate -- projection method -- alternating direction method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1244534
• Languages: English
• ISSNs: 0233-1934

Abstract

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.