Abstract
Recently, the \(l_p\) minimization problem (\(p\in (0,\,1)\)) for sparse signal recovery has been studied a lot because of its efficiency. In this paper, we propose a general smoothing algorithmic framework based on the entropy function for solving a class of \(l_p\) minimization problems, which includes the well-known unconstrained \(l_2\)–\(l_p\) problem as a special case. We show that any accumulation point of the sequence generated by the proposed algorithm is a stationary point of the \(l_p\) minimization problem, and derive a lower bound for the nonzero entries of the stationary point of the smoothing problem. We implement a specific version of the proposed algorithm which indicates that the entropy function-based algorithm is effective.
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This research was supported by the National Natural Science Foundation of China (Nos. 11171252 and 11431002).
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Li, YF., Huang, ZH. & Zhang, M. Entropy Function-Based Algorithms for Solving a Class of Nonconvex Minimization Problems. J. Oper. Res. Soc. China 3, 441–458 (2015). https://doi.org/10.1007/s40305-015-0103-1
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DOI: https://doi.org/10.1007/s40305-015-0103-1