拟凸向量值映射次微分性质及优化问题的最优性条件  

SUBDIFFERENTIAL PROPERTIES OF QUASICONVEX VECTOR VALUED MAPS AND OPTIMALITY CONDITIONS FOR OPTIMIZATION PROBLEMS

作　　者：史小波 高英 李林廷 吴春 SHI Xiao-bo;GAO Ying;LI Lin-ting;WU Chun(School of Mathematical Sciences,Chonqing 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：《数学杂志》2023年第4期336-346,共11页Journal of Mathematics

基　　金：国家自然科学基金(11771064,11991024);重庆市科学技术研究重点项目(KJZDK202001104);重庆市高校创新研究群体项目(CXQT20014);重庆市自然科学基金面上项目(cstc2019jcyj-msxmX0390);重庆市留学人员回国创业创新支持计划(cx2020096)。

摘　　要：本文研究了拟凸向量值映射的次微分及其拟凸向量优化问题的最优性条件.首先,引进恰当K-拟凸的概念,并利用△函数对其进行标量化,得到恰当K-拟凸的等价刻画.然后,给出拟凸向量值映射的四种次微分的定义,并研究了它们的性质.最后,利用拟凸向量值映射的次微分研究拟凸向量优化问题弱有效解的最优性条件,并用例子说明其合理性.In this paper we study the subdifferentiation of quasiconvex vector valued mapping and the optimality conditions of quasiconvex vector optimization problems.Firstly,we introduce the concept of proper K-quasiconvex,scalar it by using function,and obtain the equivalent characterization of proper K-quasiconvex.Then,four subdifferential definitions of quasi convex vector valued mappings are given and their properties are studied.Finally,the optimality conditions of weak efficient solutions for quasiconvex vector optimization problems are studied by using the subdifferential of quasiconvex vector valued mappings,and an example is given to illustrate its rationality.

关 键 词：拟凸向量值映射 次微分 弱有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]