A smoothing proximal gradient algorithm with extrapolation for the relaxation of $${\ell_{0}}$$ ℓ 0 regularization problem

Jie Zhang (), Xinmin Yang (), Gaoxi Li () and Ke Zhang ()
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Jie Zhang: Sichuan University
Xinmin Yang: Chongqing Normal University
Gaoxi Li: Chongqing Technology and Business University
Ke Zhang: National Center for Applied Mathematics in Chongqing

Computational Optimization and Applications, 2023, vol. 84, issue 3, No 3, 737-760

Abstract: Abstract In this paper, we consider the exact continuous relaxation model of $${\ell_{0}}$$ ℓ 0 regularization problem, which was given by Bian and Chen (SIAM J Numer Anal 58:858–883, 2020) and propose a smoothing proximal gradient algorithm with extrapolation (SPGE) for this kind of problems. Under a general choice of extrapolation parameter, it is proved that all the accumulation points have a common support set, and the ability of the SPGE algorithm to identify the zero entries of the accumulation point within finite iterations is available. We show that any accumulation point of the sequence generated by the SPGE algorithm is a lifted stationary point of the relaxation model. Moreover, a convergence rate concerning proximal residual is established. Finally, we conduct three numerical experiments to illustrate the efficiency of the SPGE algorithm compared with the smoothing proximal gradient (SPG) algorithm proposed by Bian and Chen (2020).

Keywords: Smoothing approximation; Proximal gradient method; Extrapolation; $${\ell_{0}}$$ ℓ 0 regularization problem (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-022-00446-z

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