Name
Abstract | ||
|---|---|---|
In this paper, we focus on the (ell _1-ell _p) minimization problem with (0u003cpu003c1), which is challenging due to the (ell _p) norm being non-Lipschizian. In theory, we derive computable lower bounds for nonzero entries of the generalized first-order stationary points of (ell _1-ell _p) minimization, and hence of its local minimizers. In algorithms, based on three locally Lipschitz continuous (epsilon )-approximation to (ell _p) norm, we design several iterative reweighted (ell _1) and (ell _2) methods 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 of (ell _1-ell _p) minimization. This result, in particular, applies to the iterative reweighted (ell _1) methods based on the new Lipschitz continuous (epsilon )-approximation introduced by Lu (Math Program 147(1–2):277–307, 2014), provided that the approximation parameter (epsilon ) is below a threshold value. Numerical results are also reported to demonstrate the efficiency of the proposed methods. |
Year | Venue | Field |
|---|---|---|
2018 | Comp. Opt. and Appl. | Minimization problem,Discrete mathematics,Upper and lower bounds,Mathematical analysis,Stationary point,Minification,Lipschitz continuity,Limit point,Mathematics |
DocType | Volume | Issue |
Journal | 70 | 1 |
Citations | PageRank | References |
1 | 0.36 | 5 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xianchao Xiu | 1 | 2 | 2.74 |
| Lingchen Kong | 2 | 87 | 13.42 |
| Yan Li | 3 | 399 | 95.68 |
| Houduo Qi | 4 | 437 | 32.91 |