TY - JOUR
T1 - Decomposition method for a class of monotone variational inequality problems
AU - He, B. S.
AU - Liao, L. Z.
AU - Yang, H.
N1 - Funding Information:
1The first author was supported by NSFC Grant 19671041. The second author was supported in part by Grant FRG/96-97/II 105of Hong Kong Baptist University. The third author was supported in part by UGC Grant RI94/95, EG01. 2Professor, Department of Mathematics, Nanjing University, Nanjing, P. R. China. 3Assistant Professor, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong. 4Associate Professor, Department of Civil Engineering, Hong Kong Universityof Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
PY - 1999/12
Y1 - 1999/12
N2 - In the solution of the monotone variational inequality problem VI (Ω, F), with (Formula Presented) uJ*l F(u) = \f(x)-ATy\ V = VXV, Iy J IAx-b J the augmented Lagrangian method (a decomposition method) is advantageous and effective when script Y sign = ℛm. For some problems of interest, where both the constraint sets script X sign and script Y sign are proper subsets in ℛn and ℛm, the original augmented Lagrangian method is no longer applicable. For this class of variational inequality problems, we introduce a decomposition method and prove its convergence. Promising numerical results are presented, indicating the effectiveness of the proposed method.
AB - In the solution of the monotone variational inequality problem VI (Ω, F), with (Formula Presented) uJ*l F(u) = \f(x)-ATy\ V = VXV, Iy J IAx-b J the augmented Lagrangian method (a decomposition method) is advantageous and effective when script Y sign = ℛm. For some problems of interest, where both the constraint sets script X sign and script Y sign are proper subsets in ℛn and ℛm, the original augmented Lagrangian method is no longer applicable. For this class of variational inequality problems, we introduce a decomposition method and prove its convergence. Promising numerical results are presented, indicating the effectiveness of the proposed method.
KW - Convergence
KW - Decomposition methods
KW - Monotone variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=0033259347&partnerID=8YFLogxK
U2 - 10.1023/A:1021736008175
DO - 10.1023/A:1021736008175
M3 - Journal article
AN - SCOPUS:0033259347
SN - 0022-3239
VL - 103
SP - 603
EP - 622
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -