Iterative reweighted methods for l(1) - l(p) minimization
Iterative reweighted methods for l(1) - l(p) minimization
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l(1) - l(p) 最小化的迭代重加权方法
DOI：
10.1007/s10589-017-9977-7
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发表时间：
2018
影响因子：
2.2
通讯作者：
Qi Houduo
中科院分区：
文献类型：
--
作者：
Xiu Xianchao;Kong Lingchen;Li Yan;Qi Houduo
在本文中，我们专注于最小化问题，这是具有挑战性的，由于thums是非Lipschitz的。在理论上，我们推导出可计算的下界为非零项的广义一阶稳定点ofminimization，因此其局部极小。在算法上，基于三种局部Lipschitz连续逼近问题，设计了几种迭代重加权方法来解决这些逼近问题。此外，我们证明了由这些方法产生的序列的任何聚点都是最小化的广义一阶平稳点。该结果特别适用于基于Lu（Math Program 147（1-2）：277-307，2014）引入的新Lipschitz连续近似的迭代重加权方法，前提是近似参数低于阈值。数值结果也证明了所提出的方法的效率。
In this paper, we focus on theminimization problem with, which is challenging due to thenorm being non-Lipschizian. In theory, we derive computable lower bounds for nonzero entries of the generalized first-order stationary points ofminimization, and hence of its local minimizers. In algorithms, based on three locally Lipschitz continuous-approximation tonorm, we design several iterative reweightedandmethods to solve those approximation problems. Furthermore, we show that any accumulation point of the sequence generated by these methods is a generalized first-order stationary point ofminimization. This result, in particular, applies to the iterative reweightedmethods based on the new Lipschitz continuous-approximation introduced by Lu (Math Program 147(1–2):277–307, 2014), provided that the approximation parameteris below a threshold value. Numerical results are also reported to demonstrate the efficiency of the proposed methods.