张立卫Liwei Zhang

(教授)

 博士生导师  硕士生导师
学位:博士
性别:男
毕业院校:大连理工大学
所在单位:数学科学学院
电子邮箱:lwzhang@dlut.edu.cn

论文成果

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

发表时间:2019-03-12 点击次数:

论文名称:Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming
论文类型:期刊论文
第一作者:Han, Deren
通讯作者:Han, DR (reprint author), Nanjing Normal Univ, Sch Math Sci, Key Lab NSLSCS Jiangsu Prov, Nanjing 210023, Jiangsu, Peoples R China.
合写作者:Sun, Defeng,Zhang, Liwei
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.
发表时间:2018-05-01