In this paper, we analyze the behavior of the alternating direction method of multipliers (ADMM), for solving a family of nonconvex problems. Our focus is given to the well-known consensus and sharing problems, both of which have wide applications in signal processing. We show that in the presence of nonconvex objective function, classical ADMM is able to reach the set of stationary solutions for these problems, if the stepsize is chosen large enough. An interesting consequence of our analysis is that the ADMM is convergent for a family of sharing problems, regardless of the number of blocks or the convexity of the objective function. Our analysis is broadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules.
|Original language||English (US)|
|Title of host publication||2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - Aug 4 2015|
|Event||40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia|
Duration: Apr 19 2014 → Apr 24 2014
|Name||ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings|
|Other||40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015|
|Period||4/19/14 → 4/24/14|
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© 2015 IEEE.