Dual-density-based reweighted $$\ell _{1}$$-algorithms for a class of $$\ell _{0}$$-minimization problems

Jialiang Xu, Yun-bin Zhao

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The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted ℓ1-algorithms for a class of ℓ0-minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying ℓ0-minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying ℓ0-minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted ℓ1-algorithms has also been made in this paper.
Original languageEnglish
Pages (from-to)749-772
JournalJournal of Global Optimization
Issue number3
Early online date19 Apr 2021
Publication statusE-pub ahead of print - 19 Apr 2021


  • 0-minimization
  • Bilevel optimization
  • Convex relaxation
  • Dual-density-based algorithm
  • Merit functions for sparsity
  • Strict complementarity


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