数学物理学报 ›› 2015, Vol. 35 ›› Issue (6): 1136-1145.

• 论文 • 上一篇    下一篇

一类修正邻近梯度法及其收敛性

李英毅, 张海斌, 高欢   

  1. 北京工业大学应用数理学院 北京 100124
  • 收稿日期:2014-10-14 修回日期:2015-04-27 出版日期:2015-12-25 发布日期:2015-12-25
  • 通讯作者: 张海斌,zhanghaibin@bjut.edu.cn E-mail:zhanghaibin@bjut.edu.cn
  • 作者简介:李英毅,yingyili@emails.bjut.edu.cn;高欢,huanhuan135213@163.com
  • 基金资助:

    国家自然科学基金(61179033)资助

A Modified Proximal Gradient Method and Its Convergence Rate

Li Yingyi, Zhang Haibin, Gao Huan   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124
  • Received:2014-10-14 Revised:2015-04-27 Online:2015-12-25 Published:2015-12-25

摘要:

许多现代统计和信号应用问题都可以归结为非光滑凸优化问题,该文提出了一类适用于求解非光滑凸优化问题的修正邻近梯度法.算法的特点是采用一个自适应步长,并且该算法的线性收敛性不需要目标函数的强凸性作为前提.

关键词: 非光滑凸优化, 修正邻近梯度法, 线性收敛性

Abstract:

In this paper, a modified proximal gradient method is proposed for solving a class of nonsmooth convex optimization problems, which arises in many contemporary statistical and signal applications. The proposed method adopts the self-adaptive stepsize. In addition, it is linearly convergent without the assumption of the strong convexity of the objective function.

Key words: Nonsmooth convex optimization, Modified proximal gradient method, Linear convergence

中图分类号: 

  • O224