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

Jialiang Xu () and Yun-Bin Zhao ()
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Jialiang Xu: Chinese Academy of Sciences, Beijing
Yun-Bin Zhao: Chinese University of Hong Kong

Journal of Global Optimization, 2021, vol. 81, issue 3, No 8, 749-772

Abstract: Abstract 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 $$\ell _{1}$$ ℓ 1 -algorithms for a class of $$\ell _{0}$$ ℓ 0 -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 $$\ell _{0}$$ ℓ 0 -minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying $$\ell _{0}$$ ℓ 0 -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 $$\ell _1$$ ℓ 1 -algorithms has also been made in this paper.

Keywords: Merit functions for sparsity; $$\ell _{0}$$ ℓ 0 -minimization; Dual-density-based algorithm; Strict complementarity; Bilevel optimization; Convex relaxation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-021-01013-2

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