TY - JOUR
T1 - An LQP-Based Decomposition Method for Solving a Class of Variational Inequalities
AU - Yuan, Xiaoming
AU - Li, Min
N1 - Funding information:
Corresponding author. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China ([email protected]). This author was partially supported by Hong Kong General Research Fund grant HKBU 203009 and National Natural Science Foundation of China grant 10701055.
School of Economics and Management, Southeast University, Nanjing 210096, China (limin@ seu.edu.cn). This author was supported by National Natural Science Foundation of China grant 11001053 and SRFDP grant 200802861031.
Publisher copyright:
Copyright © 2011 Society for Industrial and Applied Mathematics
PY - 2011/11/22
Y1 - 2011/11/22
N2 - The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.
AB - The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.
KW - Alternating direction method
KW - Complementarity problem
KW - Logarithmic-quadratic proximal method
KW - System of nonlinear equations
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=84862907847&partnerID=8YFLogxK
U2 - 10.1137/070703557
DO - 10.1137/070703557
M3 - Journal article
AN - SCOPUS:84862907847
SN - 1052-6234
VL - 21
SP - 1309
EP - 1318
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 4
ER -