拟凸函数的近似次微分及其在多目标优化问题中的应用  

Properties of Quasiconvex Functions and Their Applications in Multiobjective Optimization Problems

作　　者：史小波 高英 SHI Xiaobo;GAO Ying(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学和力学》2022年第3期322-329,共8页Applied Mathematics and Mechanics

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);重庆市留学人员回国创业创新支持计划(cx2020096)。

摘　　要：针对拟凸函数提出一类新的近似次微分,研究其性质,并将近似次微分应用到拟凸多目标优化问题近似解的刻画中.首先,对已有的近似次微分进行改进,得到拟凸函数新的近似次微分,并给出其与已有次微分之间的关系及一系列性质.随后,利用新的近似次微分给出拟凸多目标优化问题近似有效解、近似真有效解的最优性条件.A new type of approximate subdifferential was proposed for quasiconvex functions.Their properties were studied,and the approximate subdifferential was applied to the characterization of approximate solutions to quasiconvex multiobjective optimization problems.Firstly,the existing approximate subdifferentials were improved to get a new approximate subdifferential of the quasiconvex function,and their relationships and properties were given.Then,the optimality conditions for approximate efficient solutions and approximate properly efficient solutions to quasiconvex multiobjective optimization problems were obtained by means of the new approximate subdifferential.

关 键 词：拟凸函数 近似次微分 多目标优化问题 近似解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]