非光滑半无限多目标优化问题的对偶性  

Duality for Nonsmooth Semi-Infinite Multiobjective Optimization Problems

作　　者：杨玉红[1,2] 唐莉萍 YANG Yuhong TANG Liping(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021 School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100 College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]长江师范学院数学与统计学院,重庆408100 [3]重庆工商大学数学与统计学院,重庆400067

出　　处：《系统科学与数学》2017年第7期1633-1645,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(11431004);国家自然科学基金数学天元青年项目(11626048);重庆市科委项目(cstc2016jcyjA0178)资助课题

摘　　要：研究了一个非光滑半无限多目标优化问题(简记为SIMOP)并讨论它的对偶性.本文重点考虑此SIMOP的Mond-Weir型半无限多目标对偶问题,通过对目标函数和约束函数的某种组合赋予Clarke-凸性假设,获得了弱/强/逆对偶结论.文章的一些结论是比较新的,并推广了已有文献的一些结果.This paper deals with a nonsmooth semi-infinite multiobjective optimiza- tion problem （SIMOP, in brief） and discusses its duality. We focus on Mond-Weir type semi-infinite multiobjective dual problem of the SIMOP, and weak/strong/con- verse duality results are obtained by imposing Clarke F-convexity hypotheses on some combinations of objective functions and constraint functions. Some of our results are new and generalize the conclusions in some former literatures.

关 键 词：半无限多目标优化 对偶性 (弱)有效解 Clarke F-凸性. 

分 类 号：O221.6[理学—运筹学与控制论]