运筹学学报 ›› 2019, Vol. 23 ›› Issue (1): 35-44.doi: 10.15960/j.cnki.issn.1007-6093.2019.01.004

• 运筹学 • 上一篇    下一篇

拟凸多目标优化问题近似解的最优性条件

陈瑞婷, 徐智会, 高英*   

  1. 重庆师范大学数学科学学院, 重庆 400047
  • 收稿日期:2017-07-10 出版日期:2019-03-15 发布日期:2019-03-15
  • 通讯作者: 高英 E-mail:gaoyingimu@163.com
  • 基金资助:

    国家自然科学基金(Nos.11771064,11431004),重庆市科委项目(Nos.cstc2015jcyjA00005,cstc2018jcyj-yszxX0009),重庆市教委项目(No.KJ1500309)

The optimality conditions of approximate solutions for quasiconvex multiobjective optimization problem

CHEN Ruiting, XU Zhihui, GAO Ying*   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
  • Received:2017-07-10 Online:2019-03-15 Published:2019-03-15

摘要:

研究了拟凸多目标优化问题近似弱有效解、近似有效解的最优性条件.首先,在已有拟凸函数次微分的基础上引进4种近似次微分的概念,并给出它们之间的关系.然后,将4种近似次微分的概念应用到拟凸多目标优化问题中,给出了拟凸多目标优化问题近似弱有效解和近似有效解的充分条件和必要条件,并给出实例加以说明.

关键词: 拟凸函数, 多目标优化, 近似次微分, 近似解, 最优性条件

Abstract:

In this paper, we study the optimality conditions of approximate weak efficient solutions and approximate efficient solutions for quasiconvex multiobjective optimization problems. We introduce four concepts of approximate subdifferentials based on the existing subdifferentials of quasiconvex function, and give the relationship among them. And then, we apply these concepts to the quasiconvex multiobjective optimization problems, derive the sufficient conditions and necessary conditions for the approximate weak efficient solutions and the approximate efficient solution, and give some examples to illustrate the main results.

Key words: quasiconvex function, multiobjective optimization problems, approximate subdifferentials, approximate solutions, optimality conditions

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