A note on the smoothing quadratic regularization method for non-Lipschitz optimization

被引：4

作者：

Huang, Yakui ^{[1
]}

Liu, Hongwei ^{[1
]}

Cong, Weijie ^{[2
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China

[2] Xian Univ Posts & Telecommun, Sch Sci, Xian 710121, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2015年 / 69卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Nonsmooth nonconvex optimization; Non-Lipschitz optimization; Smoothing approximation; Quadratic regularization; WORST-CASE COMPLEXITY; VARIABLE SELECTION; NONSMOOTH; RECONSTRUCTION;

D O I：

10.1007/s11075-014-9929-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a new smaller upper bound for all the elements in the associate generalized Hessian used in the smoothing quadratic regularization (SQR) algorithm proposed by Bian and Chen (SIAM J. Optim. 23: 1718-1741, 2013). We modify the SQR algorithm by making use of the new upper bound. Numerical results show that our new upper bound improves the performance of the SQR algorithm significantly.

引用

页码：863 / 874

页数：12

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