期刊
OPTIMIZATION
卷 66, 期 7, 页码 1177-1189出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2017.1318133
关键词
Iterative soft thresholding algorithm; linear convergence analysis; linear inverse problems; sparsity pattern
资金
- National Natural Science Foundation of China [11601343, 11571308]
- Natural Science Foundation of Guangdong [2016A030310038]
- Foundation for Distinguished Young Talents in Higher Education of Guangdong [2015KQNCX145]
- MOST [105-2115-M-039-002-MY3]
The iterative soft thresholding algorithm (ISTA) is one of the most popular optimization algorithms for solving the l(1) regularized least squares problem, and its linear convergence has been investigated under the assumption of finite basis injectivity property or strict sparsity pattern. In this paper, we consider the l(1) regularized least squares problem in finite-or infinite-dimensional Hilbert space, introduce a weaker notion of orthogonal sparsity pattern (OSP) and establish the Q-linear convergence of ISTA under the assumption of OSP. Examples are provided to illustrate the cases where the linear convergence of ISTA can be established only by our result, but cannot be ensured by any existing result in the literature.
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