Adaptive projected gradient thresholding methods for constrained l0 problems

被引:4
|
作者
Zhao ZhiHua [1 ]
Xu FengMin [1 ]
Li XiangYang [1 ]
机构
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
基金
中国国家自然科学基金;
关键词
projected gradient; l(0) constraints; compressed sensing; index tracking; hard thresholding; SIGNAL RECOVERY; ALGORITHM; SHRINKAGE; RECONSTRUCTION; DECOMPOSITION; OPTIMIZATION;
D O I
10.1007/s11425-015-5038-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we propose and analyze adaptive projected gradient thresholding (APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergence will be demonstrated, and in addition, the bound of the number of iterations is established in some special cases. Under suitable assumptions, it is proved that any accumulation point of the sequence generated by the APGT methods is a local minimizer of the underdetermined linear system. Moreover, the APGT methods, under certain conditions, can find all s-sparse solutions for accurate measurement cases and guarantee the stability and robustness for flawed measurement cases. Numerical examples are presented to show the accordance with theoretical results in compressed sensing and verify high out-of-sample performance in index tracking.
引用
收藏
页码:2205 / 2224
页数:20
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