有效集方法求解欠定线性方程组的稀疏非负解
Sparse Nonnegative Solution of Underdetermined Linear Equations by Active Set Method
摘要: 针对欠定线性方程组稀疏非负解的求解问题，本文首先将原问题松弛为l0正则优化模型。随之提出有效集方法识别严格L-稳定点邻域内的零分量，基于这种快速识别技术，设计了有效集Barzilar-Borwein算法求解l0正则极小化模型。最后的数据实验证明该算法可以快速有效地求解欠定线性方程组的稀疏非负解。
Abstract: In this paper, for acquiring the sparse nonnegative solution of underdetermined linear equations, the original problem is relaxed into a l0 regularized optimization model. An active set identification technique is developed to accurately identify the zero components in a neighbourhood of the strict L-stationary point. Based on the active set identification technique, we propose an active set Barzilar-Borwein method to solve a l0 regularized minimization model. Numerical results show that the algorithm can effectively solve the sparse nonnegative solutions of underdetermined linear equations.
文章引用：张鹏, 宇振盛. 有效集方法求解欠定线性方程组的稀疏非负解[J]. 运筹与模糊学, 2020, 10(3): 172-184. https://doi.org/10.12677/ORF.2020.103018

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