Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization
- 523 Downloads
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.
KeywordsGeneralized alternating direction method of multipliers Logarithmic–quadratic proximal method Convergence rate Variational inequality
Mathematics Subject Classification90C25 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.
- 3.Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Athena Scientific, Belmont (1997)Google Scholar
- 10.Chan, T.F., Glowinski, R.: Finite element approximation and iterative solution of a class of mildly non-linear elliptic equations. Stanford University, Technical Report (1978)Google Scholar
- 23.He, B.S., Yuan, X.M.: On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers. Submission, (2013)Google Scholar
- 26.Facchinei, F., Pang, J.S.: Finite-dimensional Variational Inequalities and Complementarity Problems, Vols. I and II. Springer, New York (2003)Google Scholar