TY - JOUR
T1 - Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization
AU - Li, Min
AU - Li, Xinxin
AU - Yuan, Xiaoming
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/1
Y1 - 2015/1
N2 - We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic–quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.
AB - We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic–quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.
KW - Convergence rate
KW - Generalized alternating direction method of multipliers
KW - Logarithmic–quadratic proximal method
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=84939889767&partnerID=8YFLogxK
U2 - 10.1007/s10957-014-0567-x
DO - 10.1007/s10957-014-0567-x
M3 - Journal article
AN - SCOPUS:84939889767
SN - 0022-3239
VL - 164
SP - 218
EP - 233
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -