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
Link to Publisher's Edition
Chen, C., Li, M., & Yuan, X. (2015). 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), 906-929. https://doi.org/10.1007/s10957-014-0682-8