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Proximal ADMM with larger step size for two-block separable convex programs

Sun Min(ziyouxiaodou***at***163.com)
Sun Hongchun(sunhc68***at***126.com)
Wang Yiju(hfmaoying***at***163.com)

Abstract: The alternating direction method of multipliers (ADMM) is a benchmark for solving two-block separable convex programs, and it finds more and more applications in many areas. However, as other first-order methods, ADMM also suffers from low convergence. In this paper, to accelerate the convergence of ADMM, we relax the restriction region of the Fortin and Glowinski’s constant γ in ADMM from (0, 1+ √ 5 2 ) to (0,+∞), and thus get a proximal ADMM with larger step size. Then, to further accelerate its efficiency, we use the convex combination of its output with the current iterate to generate the new iterate. Under mild conditions, we prove the global convergence of the new method. Some numerical experiments are given to demonstrate the advantage of large step size.

Keywords: alternating direction method of multipliers; the Fortin and Glowinski’s constant; global convergence.

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 06/20/2017
Entry Accepted: 06/20/2017
Entry Last Modified: 06/20/2017

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