co-radiant集的等价表示及其在向量优化问题中的应用  

The equivalent representation of co-radiant sets and its application in multi-objective optimization problems

作　　者：汪文意 高英 刘芙萍 WANG Wenyi;GAO Ying;LIU Fuping(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《运筹学学报》2021年第2期135-143,共9页Operations Research Transactions

基　　金：国家自然科学基金(Nos.11771064,11991024);重庆市科学技术研究重点项目(No.KJZDK202001104);重庆市高校创新研究群体项目(No.CXQT20014)。

摘　　要：作为特殊的抽象凸(凹)集,radiant集和co-radiant集在抽象凸分析和多目标优化问题理论中发挥着重要作用。首先建立radiant集co-radiant集的等价刻画,从而推导出它们的重要性质。然后,将重要性质应用到向量优化问题近似解的刻画中,得到关于近似解集的等价刻画。As a special abstract convex(concave) sets,radiant sets and co-radiant sets play the important roles in abstract convex analysis and the theory of multiobjective optimization problems.We first establish the equivalent characterizations for the radiant sets and co-radiant sets.Finally,we apply important properties to the characterization of the approximate solutions of the vector optimization problems,and obtain the equivalent characterization of the approximate solution sets.

关 键 词：co-radiant集 radiant集 等价刻画 多目标优化问题 近似解 

分 类 号：O224[理学—运筹学与控制论]