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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
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.