Accelerated iterative hard thresholding algorithm for $$l_0$$l0 regularized regression problem

Fan Wu () and Wei Bian ()
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Fan Wu: Harbin Institute of Technology
Wei Bian: Harbin Institute of Technology

Journal of Global Optimization, 2020, vol. 76, issue 4, No 9, 819-840

Abstract: Abstract In this paper, we propose an accelerated iterative hard thresholding algorithm for solving the $$l_0$$l0 regularized box constrained regression problem. We substantiate that there exists a threshold, if the extrapolation coefficients are chosen below this threshold, the proposed algorithm is equivalent to the accelerated proximal gradient algorithm for solving a corresponding constrained convex problem after finite iterations. Under some proper conditions, we get that the sequence generated by the proposed algorithm is convergent to a local minimizer of the $$l_0$$l0 regularized problem, which satisfies a desired lower bound. Moreover, when the data fitting function satisfies the error bound condition, we prove that both the iterate sequence and the corresponding sequence of objective function values are R-linearly convergent. Finally, we use several numerical experiments to verify our theoretical results.

Keywords: Sparse regression problem; Accelerated iterative hard thresholding algorithm; $$l_0$$ l 0 regularization; R-linear convergence (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-019-00826-6

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