A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block

Min Li (), Defeng Sun () and Kim-Chuan Toh ()
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Min Li: School of Economics and Management, Southeast University, Nanjing 210096, P. R. China
Defeng Sun: Department of Mathematics and Risk Management Institute, National University of Singapore, 10 Lower Kent Ridge Road, Singapore
Kim-Chuan Toh: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 04, 1-19

Abstract: In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed sPADMM for the step-length $\tau \in (0, (1+\sqrt{5})/2)$ and the penalty parameter σ ∈ (0, +∞). In particular, if σ > 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block sPADMM reduces to the directly extended 3-block ADMM with $\tau \in (0, (1+\sqrt{5})/2)$.

Keywords: Convex minimization problems; alternating direction method of multipliers; semi-proximal; strongly convex; 90C25; 90C33; 65K05 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (11)

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DOI: 10.1142/S0217595915500244

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