Journal of Optimization Theory and Applications

, Volume 164, Issue 1, pp 218–233 | Cite as

Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

  • Min Li
  • Xinxin Li
  • Xiaoming YuanEmail author


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.


Generalized alternating direction method of multipliers Logarithmic–quadratic proximal method Convergence rate Variational inequality 

Mathematics Subject Classification

90C25 90C33 65K05 



The first author was supported by the National Natural Science Foundation of China Grant 11001053, the Program for New Century Excellent Talents in University Grant NCET-12-0111, and the Natural Science Foundation of Jiangsu Province grant BK2012662. The third author was partially supported by the FRG Grant from Hong Kong Baptist University: FRG2/13-14/061 and the General Research Fund from Hong Kong Research Grants Council: 203613.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Economics and ManagementSoutheast UniversityNanjingChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityHong KongChina

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