多目标优化范数标量化模型最优值的误差估计  

Error Estimation of Optimal Value of Norm Scalarization Model for Multi-Objective Optimization Problems

作　　者：夏远梅 赵克全 XIA Yuanmei;ZHAO Kequan(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《系统科学与数学》2023年第9期2319-2327,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金重大项目(11991024);国家自然科学基金项目(12171063,12101096);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(cstc2022ycjh-bgzxm0114,cstc2021jcyj-msxmX0280);重庆市教委科学技术研究项目(KJQN202100521)资助课题。

摘　　要：标量化方法是多目标优化研究的基本内容.范数标量化是研究多目标优化问题解性质与求解算法的重要方法之一.文章针对多目标优化问题的几类范数标量化模型,给出了其目标函数最优值的一些误差估计结果,进而在目标函数连续性和凸性条件下分析了误差的存在性和计算方法.Scalarization method is the basic content of the research on multi-object-ive optimization.Norm scalarization is one of the important methods to study the solution properties and solving algorithms of multi-objective optimization problems.In this paper,for several kinds of the norm scalarization models of multi-objective optimization problems,some error estimation results of the optimal values of the objective functions are given,and then the existence and calculation method of the error are analyzed under the condition of continuity and convexity of the objective functions.

关 键 词：多目标优化 范数标量化 误差估计 

分 类 号：O224[理学—运筹学与控制论]