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Hard thresholding pursuit with continuation for ℓ 0 ‐regularized minimizations
Author(s) -
Sun Tao,
Jiang Hao,
Cheng Lizhi
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5131
Subject(s) - subspace topology , continuation , regularization (linguistics) , mathematics , thresholding , convergence (economics) , algorithm , mathematical optimization , krylov subspace , iterative method , artificial intelligence , computer science , image (mathematics) , programming language , mathematical analysis , economics , economic growth
The ℓ 0 regularization has found many applications in imaging science and machine learning research for its good performance. Although the nonconvex proximal splitting method provides a way to solve it, the algorithm performs quite slowly because of that the regularization parameter is always small in applications. In view of this, in this paper, we propose a hard thresholding pursuit algorithm with continuation for the ℓ 0 ‐regularized problem. Such an algorithm has 2 steps in each iteration: in the first one, we choose a subspace by the proximal splitting; and then, we minimize the function over the subspace in the second one. We prove the convergence of this algorithm and apply it to the ℓ 0 ‐regularized least‐squares problem. Numerical results demonstrate the efficiency of this algorithm.