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Volume 44S Number 1 Volume 44 Number 1 Volume 44 Number 2

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Research articles

ScienceAsia 44 (2018): 34-39 |doi: 10.2306/scienceasia1513-1874.2018.44.034

A prediction-correction primal-dual hybrid gradient method for convex programming with linear constraints

Pibin˙Binga, Jialei˙Suia, Min˙Sunb,c,*

ABSTRACT:     In recent years, the primal-dual hybrid gradient (PDHG) method has been widely used. However, the original PDHG method may diverge without additional conditions. Here we propose a convergent prediction-correction PDHG (PD-PDHG) method for canonical convex programming with linear constraints. The most important characteristic of the PD-PDHG method is that it adopts a new descent direction in the correction step, which does not converge to zero in general. Convergence of the new method is proved under mild assumptions. Finally, its efficiency is verified by compressive sensing.

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a Institute˙of˙Electric˙Power, North˙China˙University˙of˙Water˙Resources˙and˙Electric˙Power, Zhengzhou, 450045, China
b School˙of˙Mathematics˙and˙Statistics, Zaozhuang˙University, Shandong, 277160, China
c School˙of˙Management, Qufu˙Normal˙University, Shandong, 276826, China

* Corresponding author, E-mail: ziyouxiaodou@163.com

Received 10 Jul 2017, Accepted 25 Nov 2017