TY - JOUR
T1 - New parallel descent-like method for solving a class of variational inequalities
AU - Jiang, Z. K.
AU - Yuan, X. M.
N1 - Funding Information:
Z.K. Jiang was supported by HHIT Grants KQ08013 and KX08037. X.M. Yuan was supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry; and NSFC Grant 10701055.
PY - 2010/5
Y1 - 2010/5
N2 - To solve a class of variational inequalities with separable structures, some classical methods such as the augmented Lagrangian method and the alternating direction methods require solving two subvariational inequalities at each iteration. The most recent work (B. S. He in Comput. Optim. Appl. 42(2):195-212, 2009) improved these classical methods by allowing the subvariational inequalities arising at each iteration to be solved in parallel, at the price of executing an additional descent step. This paper aims at developing this strategy further by refining the descent directions in the descent steps, while preserving the practical characteristics suitable for parallel computing. Convergence of the new parallel descent-like method is proved under the same mild assumptions on the problem data.
AB - To solve a class of variational inequalities with separable structures, some classical methods such as the augmented Lagrangian method and the alternating direction methods require solving two subvariational inequalities at each iteration. The most recent work (B. S. He in Comput. Optim. Appl. 42(2):195-212, 2009) improved these classical methods by allowing the subvariational inequalities arising at each iteration to be solved in parallel, at the price of executing an additional descent step. This paper aims at developing this strategy further by refining the descent directions in the descent steps, while preserving the practical characteristics suitable for parallel computing. Convergence of the new parallel descent-like method is proved under the same mild assumptions on the problem data.
KW - Alternating direction methods
KW - Augmented Lagrangian method
KW - Descent-like methods
KW - Parallel computing
KW - Variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=77952011738&partnerID=8YFLogxK
U2 - 10.1007/s10957-009-9619-z
DO - 10.1007/s10957-009-9619-z
M3 - Journal article
AN - SCOPUS:77952011738
SN - 0022-3239
VL - 145
SP - 311
EP - 323
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -