Convergence of the reweighted ℓ1minimization algorithm for ℓ2-ℓpminimization

Xiaojun Chen, Weijun Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

65 Citations (Scopus)

Abstract

The iteratively reweighted ℓ1minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the ℓ2-ℓpminimization problem with 0<p<1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.
Original languageEnglish
Pages (from-to)47-61
Number of pages15
JournalComputational Optimization and Applications
Volume59
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Global convergence
  • Nonsmooth and nonconvex optimization
  • Pseudo convex
  • Stationary points

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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