Department of Mathematics
Further study on the convergence rate of alternating direction method of multipliers with logarithmic-quadratic proximal regularization
© 2014, Springer Science+Business Media New York.In the literature, the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization has been proved to be convergent, and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization. Our primary purpose is to further study its convergence rate and to establish its worst-case convergence rates measured by the iteration complexity in both the ergodic and non-ergodic senses. In particular, existing convergence rate results for this combination are subsumed by the new results.
Alternating direction method of multipliers, Convergence rate, Convex programming, Iteration complexity, Logarithmic-quadratic proximal
Source Publication Title
Journal of Optimization Theory and Applications
Chen, Caihua, Min Li, and Xiaoming Yuan. "Further study on the convergence rate of alternating direction method of multipliers with logarithmic-quadratic proximal regularization." Journal of Optimization Theory and Applications 166.3 (2015): 906-929.