Department of Mathematics
An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures
Splitting methods have been extensively studied in the context of convex programming and variational inequalities with separable structures. Recently, a parallel splitting method based on the augmented Lagrangian method (abbreviated as PSALM) was proposed in He (Comput. Optim. Appl. 42:195-212, 2009) for solving variational inequalities with separable structures. In this paper, we propose the inexact version of the PSALM approach, which solves the resulting subproblems of PSALM approximately by an inexact proximal point method. For the inexact PSALM, the resulting proximal subproblems have closed-form solutions when the proximal parameters and inexact terms are chosen appropriately. We show the efficiency of the inexact PSALM numerically by some preliminary numerical experiments. © 2011 Springer Science+Business Media, LLC.
Augmented Lagrangian method, Parallel method, Prediction-correction method, Proximal point method, Splitting method, Variational inequalities
Source Publication Title
Computational Optimization and Applications
Tao, Min, and Xiaoming Yuan. "An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures." Computational Optimization and Applications 52.2 (2012): 439-461.