A parallel splitting ALM-based algorithm for separable convex programming

Xu，Shengjie1,2; He，Bingsheng3

2021

10.1007/s10589-021-00321-3

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS   影响因子和分区

0926-6003

1573-2894

The augmented Lagrangian method (ALM) provides a benchmark for solving the canonical convex optimization problem with linear constraints. The direct extension of ALM for solving the multiple-block separable convex minimization problem, however, is proved to be not necessarily convergent in the literature. It has thus inspired a number of ALM-variant algorithms with provable convergence. This paper presents a novel parallel splitting method for the multiple-block separable convex optimization problem with linear equality constraints, which enjoys a larger step size compared with the existing parallel splitting methods. We first show that a fully Jacobian decomposition of the regularized ALM can contribute a descent direction yielding the contraction of proximity to the solution set; then, the new iterate is generated via a simple correction step with an ignorable computational cost. We establish the convergence analysis for the proposed method, and then demonstrate its numerical efficiency by solving an application problem arising in statistical learning.

Augmented Lagrangian method Convex programming Jacobian decomposition Operator splitting methods Parallel computing

SCI ; EI

英语

通讯

WOS:000698996600001

20213910947561

Constrained optimization ; Convergence of numerical methods ; Lagrange multipliers

Numerical Methods:921.6 ; Systems Science:961

ENGINEERING

2-s2.0-85115679030

Scopus

1.Department of Mathematics,Harbin Institute of Technology,Harbin,China
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Department of Mathematics,Nanjing University,Nanjing,China

Xu，Shengjie,He，Bingsheng. A parallel splitting ALM-based algorithm for separable convex programming[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2021,80:831-851.

Xu，Shengjie,&He，Bingsheng.(2021).A parallel splitting ALM-based algorithm for separable convex programming.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,80,831-851.

Xu，Shengjie,et al."A parallel splitting ALM-based algorithm for separable convex programming".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 80(2021):831-851.