Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/78064
Title: Linear rate convergence of the alternating direction method of multipliers for convex composite programming
Authors: Han, D
Sun, D 
Zhang, L
Keywords: ADMM
Calmness
Q-linear convergence
Multiblock
Composite conic programming
Issue Date: 2018
Publisher: Institute for Operations Research and the Management Sciences
Source: Mathematics of operations research, 2018, v. 43, no. 2, p. 622-637 How to cite?
Journal: Mathematics of operations research 
Abstract: In this paper, we aim to prove the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a mild calmness condition, which holds automatically for convex composite piecewise linear-quadratic programming, we establish the global Q-linear rate of convergence for a general semi-proximal ADMM with the dual step-length being taken in (0, (1 + 5(1/2))/2). This semi-proximal ADMM, which covers the classic one, has the advantage to resolve the potentially nonsolvability issue of the sub-problems in the classic ADMM and possesses the abilities of handling the multi-block cases efficiently. We demonstrate the usefulness of the obtained results when applied to two- and multi-block convex quadratic (semidefinite) programming.
URI: http://hdl.handle.net/10397/78064
ISSN: 0364-765X
EISSN: 1526-5471
DOI: 10.1287/moor.2017.0875
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