A shrinkage-thresholding projection method for sparsest solutions of LCPs

被引：5

作者：

Shang, Meijuan ^{[1
,2
]}

Nie, Cuiping ^{[2
]}

机构：

[1] Beijing Jiaotong Univ, Dept Appl Math, Beijing 100044, Peoples R China

[2] Shijiazhuang Univ, Dept Math, Shijiazhuang 050035, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2014年

基金：

中国国家自然科学基金;

关键词：

linear complementarity problems; sparsest solutions; l(1) regularized minimization; shrinkage-thresholding operator; convergence; INVERSE PROBLEMS; ALGORITHM;

D O I：

10.1186/1029-242X-2014-51

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the sparsest solutions of linear complementarity problems (LCPs), which study has many applications, such as bimatrix games and portfolio selections. Mathematically, the underlying model is NP-hard in general. By transforming the complementarity constraints into a fixed point equation with projection type, we propose an l(1) regularization projection minimization model for relaxation. Through developing a thresholding representation of solutions for a key subproblem of this regularization model, we design a shrinkage-thresholding projection (STP) algorithm to solve this model and also analyze convergence of STP algorithm. Numerical results demonstrate that the STP method can efficiently solve this regularized model and get a sparsest solution of LCP with high quality.

引用

页数：10