Accelerated iterative hard thresholding algorithm for l0 regularized regression problem

In this paper, we propose an accelerated iterative hard thresholding algorithm for solving the l 0 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...

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Bibliographic Details
Published in:Journal of global optimization Vol. 76; no. 4; pp. 819 - 840
Main Authors: Wu, Fan, Bian, Wei
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2020
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Convergence
Iterative methods
Lower bounds
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
R-linear convergence
Sparse regression problem
Accelerated iterative hard thresholding algorithm
regularization
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we propose an accelerated iterative hard thresholding algorithm for solving the l 0 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 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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-019-00826-6