Sciweavers

Share
MP
2016

The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent

4 years 3 months ago
The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent
The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend the ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of more than two separable convex functions. However, the convergence of this extension has been missing for a long time — neither an affirmative convergence proof nor an example showing its non-convergence is known in the literature. In this paper we give a negative answer to this long-standing open question: The direct extension of ADMM is not necessarily convergent. We present a sufficient condition to ensure the convergence of the direct extension of ADMM, and give an example to show its divergence. Keywords. Alternating direction method of multipliers, Convergence analysis, Convex programming, Splitting methods
Caihua Chen, Bingsheng He, Yinyu Ye, Xiaoming Yuan
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where MP
Authors Caihua Chen, Bingsheng He, Yinyu Ye, Xiaoming Yuan
Comments (0)
books