无限指标集上的择一定理及其在向量优化中的应用  

Alternative Theorem on Infinite Index Set and Its Application in Vector Optimization

作　　者：陈磊 高英 CHEN Lei;GAO Ying(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：《重庆师范大学学报（自然科学版）》2021年第3期1-5,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.1771064,No.1991024);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);重庆市留学人员回国创业创新支持计划(No.CX2020096)。

摘　　要：【目的】探究无限多个准则的向量优化问题解的刻画。【方法】通过建立无限指标集上的择一定理,研究了无限多个准则的向量优化问题的弱有效解、有效解和G-真有效解的标量化刻画。【结果】首先,在不需要任何凸性条件下建立了无限指标集上的择一定理。随后,将择一定理应用到无限多个准则的向量优化问题中,给出了弱有效解、有效解和G-真有效解的标量化结果。【结论】所得结果对处理无限多个准则的向量优化问题具有实际意义。[Purposes]Exploring the characterization description of the solution to the vector optimization problem with infinite multiple criteria.[Methods]Establishing an alternative theorem on an infinite index set,studying the characterization of weak efficient solution,efficient solution and G-proper efficient solution of the vector optimization problem with infinite multiple criteria.[Findings]First of all,the alternative theorem on the infinite index set is established without any convexity.Subsequently,the alternative theorem is applied to the vector optimization problem of infinite multiple criteria,and the scalarized results for the weak efficient solution,the efficient solution and G-proper efficient solution are given.[Conclusions]It has practical significance for dealing with vector optimization problems with infinite multiple criteria.

关 键 词：无限指标集 择一定理 向量优化 标量化方法 

分 类 号：O221.6[理学—运筹学与控制论]