TY - JOUR
T1 - An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures
AU - Tao, Min
AU - Yuan, Xiaoming
N1 - Funding Information:
Acknowledgements Min Tao was supported by the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY210049) and the NSFC Grant 10971095. Xiaoming Yuan was supported by a Hong Kong General Research Fund.
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
KW - Augmented Lagrangian method
KW - Parallel method
KW - Prediction-correction method
KW - Proximal point method
KW - Splitting method
KW - Variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=84861879364&partnerID=8YFLogxK
U2 - 10.1007/s10589-011-9417-z
DO - 10.1007/s10589-011-9417-z
M3 - Journal article
AN - SCOPUS:84861879364
SN - 0926-6003
VL - 52
SP - 439
EP - 461
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
IS - 2
ER -