Abstract
© 2016 Societ y for Industrial and Applied Mathematics.This paper presents a majorized alternating direc tion method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained 2-block convex composite optimization problems with each block in the objective being the sum of a nonsmooth convex function (p(x) or q (y)) and a smooth convex function (f(x) or g(y)), i.e., min??, y?y{p(x) + f(x) + q(y) + g (y) | A?x + B?y = c}. By choosing the indefinite proximal terms properly, we establish the global convergence and the iteration-complexity in the nonergodic sense of the proposed method for the step-length ? ? (0, (1 + ?5)/2). The computational benefit of using indefinite proximal terms within the ADMM framework instead of the current requirement of positive semidefinite ones is also demonstrated numerically. This opens up a new way to improve the practical performance of the ADMM and related methods.
Original language | English |
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Pages (from-to) | 922-950 |
Number of pages | 29 |
Journal | SIAM Journal on Optimization |
Volume | 26 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2016 |
Externally published | Yes |
Keywords
- Alternating direction method of multipliers
- Convex composite optimization
- Indefinite proximal terms
- Iteration-complexity
- Majorization
ASJC Scopus subject areas
- Software
- Theoretical Computer Science