TY - JOUR
T1 - Decomposition method for a class of monotone variational inequality problems
AU - He, B. S.
AU - Liao, L. Z.
AU - Yang, H.
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sets script X sign and script Y sign are proper subsets in ℛn and ℛm, the original augmented Lagrangian method is no longer applicable.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sets script X sign and script Y sign are proper subsets in ℛn and ℛm, the original augmented Lagrangian method is no longer applicable.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 - https://www.webofscience.com/wos/woscc/full-record/WOS:000084207300006
UR - https://openalex.org/W122578774
UR - https://www.scopus.com/pages/publications/0033259347
U2 - 10.1023/A:1021736008175
DO - 10.1023/A:1021736008175
M3 - Journal Article
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 -