上海大学学报(自然科学版) ›› 2012, Vol. 18 ›› Issue (1): 59-63.doi: 10.3969/j.issn.1007-2861.2012.01.012

• 论文 • 上一篇    下一篇

基于一种新的γ-扩张凹极小化问题的割平面算法

刘林娜,杨永建,余峰   

  1. 上海大学 理学院,上海 200444
  • 收稿日期:2010-09-10 出版日期:2012-02-29 发布日期:2012-02-29
  • 通讯作者: 杨永建(1966~),男,副教授,研究方向为运筹学和控制论. E-mail:yjyang@mail.shu.edu.cn E-mail:yjyang@mail.shu.edu.cn

Cutting Plane Method for Solving Concave Minimization Programming Based on a New γ-Extension

LIU Lin-na,YANG Yong-jian,YU Feng   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2010-09-10 Online:2012-02-29 Published:2012-02-29

摘要: 首先,介绍凹极小化问题的有关内容及割平面算法的思想.然后,给出一种变上限函数积分法,并利用该积分法来求解凹极小化过程中γ-扩张的γ数.新算法在有限步内得到原问题的一个近似最优解,且算法的近似最优解为全局最优解.最后,通过数值试验证明了新算法是可行有效的.

关键词: -扩张, &gamma, 凹极小化, 变上限积分函数法, 割平面算法

Abstract: We first briefly give the concept of concave minimization programming and the cutting plane method, and then propose the uncertain upper limited integral function method which will be used to solve γ constant in the γ-extension. We show that the proposed method only requires a finite number of iterations to reach a near-optimal solution that is just the global optimization. Implementation of the method is reported with satisfactory numerical results.

Key words: γ-extension, concave minimization, cutting plane method, uncertain upper limited integral function method

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