An Iterative Threshold Algorithm Based on Log-sum Regularization.pdf (208.66 kB)
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An Iterative Threshold Algorithm of Log-sum Regularization for Sparse Problem

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posted on 2022-11-02, 03:05 authored by xin zhouxin zhou, Xiaowen Liu, Gong Zhang, Luliang Jia, Xu Wang, Zhiyuan Zhao

The log-sum regularization has been always drawing widespread attention in the field of sparse problem. However, it brings about a non-convex, non-smooth, and non-Lipschitz optimization problem that is difficult to tackle. To overcome the problem, an iterative threshold algorithm of log-sum regularization is proposed in this paper. Firstly, by deducing the derivative mathematical expression of log-sum function, a property theorem about solution for log-sum regularization is established. Secondly, based on the above theorem, the optimal setting rules of the compromising parameters are elaborated, and the iterative log-sum threshold algorithm is proposed. Thirdly, under the situation that the compromising parameters of log-sum regularization are relatively small, it can be proven that the proposed algorithm converges to a local minimizer of log-sum regularization. Finally, a series of simulations are implemented to examine performance of the algorithm, and the results exhibit that the proposed algorithm outperforms the state-of-the-art algorithms in terms of iterations and precision.


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the College of Information and Communication, National University of Defense Technology

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  • China