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Indexed by:Journal Papers

Date of Publication:2020-07-01

Journal:MATHEMATICS OF COMPUTATION

Included Journals:SCIE

Volume:89

Issue:324

Page Number:1867-1894

ISSN No.:0025-5718

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

Abstract: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.