一类特殊优化问题的光滑梯度法

doi:10.15960/j.cnki.issn.1007-6093.2017.02.013

运筹学学报

一类特殊优化问题的光滑梯度法

陈元媛^1,2,* 高岩¹ 刘志敏² 杜守强²

1. 上海理工大学管理学院, 上海 200093; 2. 青岛大学数学与统计学院, 山东青岛 266071

收稿日期:2017-03-30 出版日期:2017-06-15 发布日期:2017-06-15
通讯作者: 陈元媛 E-mail: usstchenyuanyuan@163.com
基金资助:
国家自然科学基金(Nos.11671220, 11401331), 山东省自然科学基金(No. ZR2016AM29)

The smoothing gradient method for a kind of special optimization problem

CHEN Yuanyuan^1,2,* GAO Yan¹ LIU Zhimin² DU Shouqiang²

1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China; 2. College of Mathematics and Statistic, Qingdao University, Qingdao 266071, Shangdong, China

Received:2017-03-30 Online:2017-06-15 Published:2017-06-15

摘要/Abstract

摘要：

对一类在压缩感知、图像处理等相关领域有广泛应用的特殊非光滑优化问题进行了研究, 给出了求解此类问题的光滑梯度法及算法的全局收敛性证明, 相关的数值实验表明算法的有效性.

关键词: 非光滑优化, 光滑梯度法, 全局收敛

Abstract:

In this paper, we study a kind of special nonsmooth optimization problem, which is widely used in the field of compressed sensing and image processing. A smoothing gradient method is proposed and the global convergence is also given. Finally, the related numerical results indicate the efficiency of the given method.

Key words: nonsmooth optimization, smoothing gradient method, global convergence

陈元媛, 高岩, 刘志敏, 杜守强. 一类特殊优化问题的光滑梯度法[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.013.

CHEN Yuanyuan, GAO Yan, LIU Zhimin, DU Shouqiang. The smoothing gradient method for a kind of special optimization problem[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.013.

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一类特殊优化问题的光滑梯度法

The smoothing gradient method for a kind of special optimization problem

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