- Global Convergence of ADMM in Nonconvex Nonsmooth Optimization Yu Wang(shifwanggmail.com) Wotao Yin(wotaoyinucla.edu) Jinshan Zeng(jinshanzengjxnu.edu.cn) 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, $\phi(x_1,\ldots,x_p,y)$, subject to linear equality constraints that couple $x_1,\ldots,x_p,y$, where $p\ge 1$ is an integer. Our ADMM sequentially updates the primal variables in the order $x_1,\ldots,x_p,y$, 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: Nonlinear Optimization Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 3: Nonlinear Optimization (Other ) Citation: UCLA CAM Report 15-61, 2015 Download: [PDF]Entry Submitted: 11/28/2015Entry Accepted: 11/28/2015Entry Last Modified: 11/28/2015Modify/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.