点击次数：

论文类型：期刊论文

发表时间：2020-07-01

发表刊物：MATHEMATICS OF COMPUTATION

收录刊物：SCIE

卷号：89

期号：324

页面范围：1867-1894

ISSN号：0025-5718

关键字：Alternating direction method of multiplier; linear rate convergence; indefinite proximal term; logistic regression; symmetric Gauss-Seidel decomposition

摘要：This paper aims to study a majorized alternating direction method of multipliers with indefinite proximal terms (iPADMM) for convex composite optimization problems. We show that the majorized iPADMM for 2-block convex optimization problems converges globally under weaker conditions than those used in the literature and exhibits a linear convergence rate under a local error bound condition. Based on these, we establish the linear rate convergence results for a symmetric Gauss-Seidel based majorized iPADMM, which is designed for multiblock composite convex optimization problems. Moreover, we apply the majorized iPADMM to solve different types of regularized logistic regression problems. The numerical results on both synthetic and real datasets demonstrate the efficiency of the majorized iPADMM and also illustrate the effectiveness of the introduced indefinite proximal terms.