A Linearized Alternating Direction Method of Multipliers with Substitution Procedure

Miantao Chao (), Caozong Cheng () and Haibin Zhang ()
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Miantao Chao: Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China
Caozong Cheng: Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China
Haibin Zhang: Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 03, 1-19

Abstract: We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m ≥ 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m ≥ 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

Keywords: Alternating direction method of multipliers; convex programming; convergence rate; contraction methods (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915500116

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