A shrinkage-thresholding projection method for sparsest solutions of LCPs

作者：Shang Meijuan^*; Nie Cuiping

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 2014(1): 51.

DOI：10.1186/1029-242X-2014-51

• linear complementarity problems
• sparsest solutions
• l(1) regularized minimization
• shrinkage-thresholding operator
• convergence

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.

• 出版日期2014-1-31
• 单位石家庄学院; 北京交通大学