- Global Convergence of ADMM in Nonconvex Nonsmooth Optimization Yu Wang (wang.yuberkeley.edu) Wotao Yin (wotaoyinucla.edu) Jinshan Zeng (jsh.zenggmail.com) Abstract: In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $\phi(x_0,\ldots,x_p,y)$, subject to coupled linear equality constraints. Our ADMM updates each of the primal variables $x_0,\ldots,x_p,y$, followed by updating the dual variable. We separate the variable $y$ from $x_i$'s as it has a special role in our analysis. The developed convergence guarantee covers a variety of nonconvex functions such as piecewise linear functions, $\ell_q$ quasi-norm, Schatten-$q$ quasi-norm (\$0 Keywords: ADMM, nonconvex optimization, augmented Lagrangian method, block coordinate descent, sparse optimization Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Download: [PDF]Entry Submitted: 11/26/2016Entry Accepted: 11/26/2016Entry Last Modified: 12/06/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.