一种求解弹性l_2-l_q正则化问题的算法

doi:10.15960/j.cnki.issn.1007-6093.2016.04.002

运筹学学报

一种求解弹性l_2-l_q正则化问题的算法

张勇¹ 叶万洲^1,*

1. 上海大学数学系, 上海 200444

收稿日期:2016-03-18 出版日期:2016-12-15 发布日期:2016-12-15
通讯作者: 叶万洲 wzhy@shu.edu.cn
基金资助:
国家自然科学基金(No. 61071186)

An algorithm for elastic l_2-l_q regularization

ZHANG Yong¹ YE Wanzhou^1,*

1. Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2016-03-18 Online:2016-12-15 Published:2016-12-15

摘要/Abstract

摘要：

给出了一种求解弹性l_{2}-l_{q}正则化问题的迭代重新加权l_{1}极小化算法, 并证明了由该算法产生的迭代序列是有界且渐进正则的. 对于任何有理数q\in(0,1), 基于一个代数的方法, 进一步证明了迭代重新加权l_{1}极小化算法收敛到弹性l_{2}-l_{q}(0<q<1)正则化问题的稳定点. 最后, 通过稀疏信号恢复的数值实例验证了算法的有效性.

关键词: l_{q}正则化, 迭代重新加权l_{1}极小化算法, 非凸优化

Abstract:

In this paper, we present an iteratively re-weighted l_{1} minimization (IRL1) algorithm for solving elastic l_{2}-l_{q} regularization. We prove that any sequence generated by the IRL1 algorithm is bounded and asymptotically regular. We further prove that the sequence is convergent based on an algebraic method for any rational q \in (0,1) and the limit is a stationary point of the elastic l_{2}-l_{q}(0<q<1) minimization problem. Numerical experiments on sparse signal recovery are presented to demonstrate the effectiveness of the proposed algorithm.

Key words: l_{q} regularization, IRL1 algorithm, nonconvex optimization

张勇, 叶万洲. 一种求解弹性l_2-l_q正则化问题的算法[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.04.002.

ZHANG Yong, YE Wanzhou. An algorithm for elastic l_2-l_q regularization[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.04.002.

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一种求解弹性l_2-l_q正则化问题的算法

An algorithm for elastic l_2-l_q regularization

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