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Entropy Function-Based Algorithms for Solving a Class of Nonconvex Minimization Problems

  • Yu-Fan Li
  • Zheng-Hai HuangEmail author
  • Min Zhang
Article

Abstract

Recently, the \(l_p\) minimization problem (\(p\in (0,\,1)\)) for sparse signal recovery has been studied a lot because of its efficiency. In this paper, we propose a general smoothing algorithmic framework based on the entropy function for solving a class of \(l_p\) minimization problems, which includes the well-known unconstrained \(l_2\)\(l_p\) problem as a special case. We show that any accumulation point of the sequence generated by the proposed algorithm is a stationary point of the \(l_p\) minimization problem, and derive a lower bound for the nonzero entries of the stationary point of the smoothing problem. We implement a specific version of the proposed algorithm which indicates that the entropy function-based algorithm is effective.

Keywords

\(l_p\) minimization problem Entropy function Smoothing conjugate gradient method 

Mathematics Subject Classification

65K05 90C26 90C59 

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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceTianjin UniversityTianjinChina
  2. 2.Center for Applied Mathematics of Tianjin UniversityTianjinChina

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