English

运筹学学报 ›› 2015, Vol. 19 ›› Issue (2): 105-110.doi: 10.15960/j.cnki.issn.1007-6093.2015.02.012

• 运筹学 • 上一篇    下一篇

向量优化问题 (C,\varepsilon)-弱有效解的一种非线性标量化性质

郭辉1,2,*   

  1. 1. 上海大学理学院, 上海  200444; 2. 重庆师范大学数学学院, 重庆  400047
  • 收稿日期:2014-04-18 出版日期:2015-06-15 发布日期:2015-06-15
  • 通讯作者: 郭辉 guoguofly@163.com
  • 基金资助:

    1. 国家自然科学基金(Nos. 11301574, 11271391);
    2. 重庆市重点科技项目(No. 2011BA0030)

A characterization of weakly (C,\varepsilon)-efficient solution of vector optimization via nonlinear scalarization

GUO Hui1,2,*   

  1. 1. College of Sciences, Shanghai University, Shanghai 200444, China; 2. College of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
  • Received:2014-04-18 Online:2015-06-15 Published:2015-06-15

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摘要：

Guti\'{e}rrez 等在 co-radiant 集的基础上提出了一种新的 (C,\varepsilon)-弱有效解, 它统一了之前文献中提出的几种经典的近似解. 利用由 G\"{o}pfert 等提出的一类非线性标量化函数, 给出了 (C,\varepsilon)-弱有效解的一个等价性质. 最后, 给出一个例子说明主要结果.

关键词: (C,\varepsilon)-弱有效解, 非线性标量化, 向量优化

Abstract:

Recently, Guti\'{e}rrez et al. proposed a new type of efficiency based on co-radiant set which called (C,\varepsilon)-efficient solution in vector optimization. This new notion of efficiency unifies some well-known concepts introduced previously in the literature. In this paper, we characterizes the new (C,\varepsilon)-efficient solution by a nonlinear scalarization function proposed by G\"{o}pfert, et al. Furthermore, an example is given to illustrate our main result.

Key words: weakly (C,\varepsilon)-efficient solution, nonlinear scalarization, vector optimization