• 论文 •

### 稀疏线性规划研究

1. 1. 中国科学院数学与系统科学研究院, 北京 100190;
2. 中国科学院大学数学科学学院, 北京 100049;
3. 西安交通大学经济与金融学院, 西安 710049
• 收稿日期:2017-12-30 出版日期:2018-12-15 发布日期:2018-11-20
• 通讯作者: 徐凤敏,Email:fengminxu@mail.xjtu.edu.cn
• 基金资助:

国家973项目（2015CB856002），国家自然科学基金重点项目（11631013），国家自然科学基金（11571271）.

Chen Shengjie, Dai Yuhong, Xu Fengmin. ON THE STUDY OF SPARSE LINEAR PROGRAMMING[J]. Mathematica Numerica Sinica, 2018, 40(4): 339-353.

### ON THE STUDY OF SPARSE LINEAR PROGRAMMING

Chen Shengjie1,2, Dai Yuhong1,2, Xu Fengmin3

1. 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710049, China
• Received:2017-12-30 Online:2018-12-15 Published:2018-11-20

Sparse linear programming is widely used in computational finance, industrial production, assembly scheduling and other fields. This paper proposes the general model of sparse linear programming problem and shows that the problem is NP-hard. Then we use alternating direction method of multipliers (ADMM) to solve it and prove the convergence of the algorithm in the approximate form. Numerical experiments show that the ADMM algorithm performs better than the hybrid genetic algorithm for large-scale numerical examples. Meanwhile, the good performance of the algorithm in financial cases verifies the validity of the algorithm and the model for solving sparse portfolio problems.

MR(2010)主题分类:

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