A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING

He, Bingsheng1; Ma, Feng2; Xu, Shengjie3,4; Yuan, Xiaoming5

2023-02-01

10.1090/mcom/3822

MATHEMATICS OF COMPUTATION   Impact Factor & Quartile

0025-5718

1088-6842

The augmented Lagrangian method (ALM) is classic for canoni-cal convex programming problems with linear constraints, and it finds many applications in various scientific computing areas. A major advantage of the ALM is that the step for updating the dual variable can be further relaxed with a step size in (0, 2), and this advantage can easily lead to numerical ac-celeration for the ALM. When a separable convex programming problem is discussed and a corresponding splitting version of the classic ALM is consid-ered, convergence may not be guaranteed and thus it is seemingly impossible that a step size in (0,2) can be carried on to the relaxation step for updating the dual variable. We show that for a parallel splitting version of the ALM, a step size in (0,2) can be maintained for further relaxing both the primal and dual variables if the relaxation step is simply corrected by a rank-two matrix. Hence, a rank-two relaxed parallel splitting version of the ALM with a step size in (0,2) is proposed for separable convex programming problems. We validate that the new algorithm can numerically outperform existing algorithms of the same kind significantly by testing some applications.

Convex programming scientific computing augmented Lagrangian method parallel splitting step size

SCI

English

Others

NSFC["11871029","12171481","11871264"]

Mathematics

Mathematics, Applied

WOS:000941193400001

AMER MATHEMATICAL SOC

MATHEMATICS

Web of Science

1.Nanjing Univ, Dept Math, Nanjing, Peoples R China
2.High Tech Inst Xian, Xian 710025, Shaanxi, Peoples R China
3.Harbin Inst Technol, Dept Math, Harbin, Peoples R China
4.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
5.Univ Hong Kong, Dept Math, Hong Kong, Peoples R China

He, Bingsheng,Ma, Feng,Xu, Shengjie,et al. A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING[J]. MATHEMATICS OF COMPUTATION,2023.

He, Bingsheng,Ma, Feng,Xu, Shengjie,&Yuan, Xiaoming.(2023).A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING.MATHEMATICS OF COMPUTATION.

He, Bingsheng,et al."A RANK-TWO RELAXED PARALLEL SPLITTING VERSION OF THE AUGMENTED LAGRANGIAN METHOD WITH STEP SIZE IN (0,2) FOR SEPARABLE CONVEX PROGRAMMING".MATHEMATICS OF COMPUTATION (2023).