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运筹学学报 >

2016 , Vol. 20 >Issue 2: 113 - 120

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.02.011

运筹学

求解非光滑凸规划的一种混合束方法

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  • 1. 上海理工大学管理学院, 上海 200093

收稿日期: 2014-10-13

  网络出版日期: 2016-06-15

基金资助

国家自然科学基金(No. 11171221), 上海市一流学科项目(No. XTKX2012), 高等学校博士学科点专项科研基金(No. 20123120110004)

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A hybrid bundle method for nonsmooth convex optimization

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  • 1. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received date: 2014-10-13

  Online published: 2016-06-15

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摘要

提出一种求解非光滑凸规划问题的混合束方法. 该方法通过对目标函数增加迫近项, 且对可行域增加信赖域约束进行迭代, 做为迫近束方法与信赖域束方法的有机结合, 混合束方法自动在二者之间切换, 收敛性分析表明该方法具有全局收敛性. 最后的数值算例验证了算法的有效性．

关键词： 非光滑优化; 迫近束方法; 信赖域束方法

本文引用格式

张清叶, 高岩 . 求解非光滑凸规划的一种混合束方法[J]. 运筹学学报, 2016 , 20(2) : 113 -120 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.02.011

Abstract

A hybrid bundle method for nonsmooth convex optimization problems is proposed. In this method, the next iterate point is obtained by solving a subproblem which is formed by adding proximal term to the objective function and trust region constraint to the feasible region. The proposed algorithm combines proximal bundle method with trust region bundle method and switches between them automatically. Convergence analysis shows that the algorithm we proposed is global convergent. Finally, a numerical example is given to verify the validity of the method we proposed.

Key words： nonsmooth optimization; proximal bundle method; trust region bundle method

参考文献

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[8] 高岩. 非光滑优化 [M]. 北京：科学出版社, 2008.
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[10] Shen J, Li D, Pang L P. A cutting plane and level stabilization bundle method with inexact data for minimizing nonsmooth nonconvex functions [J].  Abstract and Applied Analysis, 2014, Doi:10.1155/2014/192893.
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