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Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming

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论文类型:期刊论文

发表时间:2018-05-01

发表刊物:MATHEMATICS OF OPERATIONS RESEARCH

收录刊物:SCIE

文献类型:J

卷号:43

期号:2

页面范围:622-637

ISSN号:0364-765X

关键字:ADMM; calmness; Q-linear convergence; multiblock; composite conic programming

摘要: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.

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