华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 1: 43 - 50

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.01.006

应用数学与基础数学

一类非光滑分式优化问题的最优性条件和对偶

  • 王国栋 ,
  • 陈林
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  • 1. 重庆水利电力职业技术学院, 重庆402160; 2. 四川大学~数学学院, 成都610065)
王国栋, 男, 硕士, 讲师, 研究方向为优化理论及应用.

收稿日期: 2014-11-04

  网络出版日期: 2016-03-10

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Optimality conditions and duality for a class of non-smooth fractional optimization problems

  • WANG Guo-Dong ,
  • CHEN Lin
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Received date: 2014-11-04

  Online published: 2016-03-10

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摘要

研究了一类非光滑多目标分式优化问题,利用变分分析和广义微分中的工具, 在新的凸性假设下,建立了此类优化问题有效解的必要条件和充分条件.这些结果都是用极限次微分来刻画的,这在非光滑多目标分式优化问题的研究中是一个比较新的结果,而对于极限次微分的研究是近年来国内外优化领域的研究学者比较关注的一个课题.此外, 文中第二部分提出了此类优化问题的~Mond-Weir~对偶模型,并研究了弱对偶、强对偶的结果.

关键词： 非光滑; 极限次微分; 广义凸; 对偶

本文引用格式

王国栋 , 陈林 . 一类非光滑分式优化问题的最优性条件和对偶[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(1) : 43 -50 . DOI: 10.3969/j.issn.1000-5641.2016.01.006

Abstract

This paper studies a class of non-smooth multi-objective fractional optimization problems, using the tools in variational analysis and the generalized differential, and establishes necessary conditions and sufficient conditions under some new convexity. These results, which are relatively new in the study of non-smooth multi-objective fractional optimization problems, are characterized by limiting subdifferential. And the study of limiting subdifferential is a pretty hot subject in recent years. In addition, the weak duality and the strong duality results have been obtained in Mond-Weir type duality.

Key words： non-smooth; limiting subdifferential; generalized convexity; duality

参考文献

[1] MORDUKHOVICH B S. Variational Analysis and Generalized Differentiation I: Basic Theory [M]. Berlin: Springer, 2006.
[2] CLARKE F H. Optimization and Nonsmooth Analysis [M]. New York: Wiley-Interscience, 1983.
[3] ROCKAFELLAR R T. Convex Analysis [M]. Princeton: Princeton University Press, 1970.
[4] CHEN G Y, HUANG X X, YANG X Q. Vector Optimization: Set-Valued and Variational Analysis [M]. Berlin: Springer-Verlag, 2005.
[5] SOGHORA N. Optimatlity and duality for nonsmooth multiobjective fractional programming with mixed constraints [J]. J Glob Optim, 2008, 41: 103-115.
[6] CHUONG T D, KIM D S. Nonsmooth semi-infinite multiobjective optimization problems [J]. J Optim Theory Appl, 2014, 160: 748-762.
[7] CHUONG T D, KIM D S. Optimality conditions and duality in nonsmooth multiobjective optimization problems [J]. Annals of Operations Research, 2014, 217(1): 117-136.
 
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