定向距离函数的光滑化方法及其应用

doi:10.15960/j.cnki.issn.1007-6093.2024.02.009

运筹学学报（中英文） ›› 2024, Vol. 28 ›› Issue (2): 117-130.doi: 10.15960/j.cnki.issn.1007-6093.2024.02.009

定向距离函数的光滑化方法及其应用

李鑫怡¹, 高英²^,*(), 赵春杰³

1. 重庆师范大学数学科学学院, 重庆 401331
2. 内蒙古大学数学科学学院, 内蒙古呼和浩特 010021
3. 成都石室东部新区实验学校, 四川成都 641419

收稿日期:2022-11-01 出版日期:2024-06-15 发布日期:2024-06-07
通讯作者: 高英 E-mail:gaoyingimu@163.com
基金资助:
国家自然科学基金(11991024);国家自然科学基金(12171063);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)

The smoothing method of the oriented distance function and its application

Xinyi LI¹, Ying GAO²^,*(), Chunjie ZHAO³

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
2. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, Inner Mongolia, China
3. Eastern New Centre Experimental School of Chengdu Shishi, Chengdu 641419, Sichuan, China

Received:2022-11-01 Online:2024-06-15 Published:2024-06-07
Contact: Ying GAO E-mail:gaoyingimu@163.com

摘要/Abstract

摘要：

本文考虑定向距离函数的光滑化表示及其应用。首先在已有的两种光滑化方法的基础上, 给出了这类特殊的非光滑函数的光滑化表示。作为特例, 在二维空间中, 给出该函数更具体的光滑化函数。最后利用定向距离函数的光滑化函数以及它在多目标优化问题标量化方法中的应用, 建立非光滑多目标优化问题的光滑标量化模型, 并给出了两者之间解集的关系。

关键词: 定向距离函数, 光滑化方法, 非光滑多目标优化问题, 近似解

Abstract:

This paper considers the smooth representation of the oriented distance function and its application. On the basis of two existing smoothing methods, the smoothing representation of this special non-smooth function is given. As a special case, a more specific smoothing function of this function is given in two dimensional space. Finally, by using the smoothing function of the oriented distance function and its application in the scaling method of multi-objective optimization problem, we study the non-smooth multi-objective optimization problem and the corresponding smooth single-objective optimization problem, and give the relationship between the solution sets of the two problems.

Key words: the oriented distance function, smoothing method, nonsmooth multi-objective optimization problem, the approximate solutions

中图分类号:

O221.6

李鑫怡, 高英, 赵春杰. 定向距离函数的光滑化方法及其应用[J]. 运筹学学报（中英文）, 2024, 28(2): 117-130.

Xinyi LI, Ying GAO, Chunjie ZHAO. The smoothing method of the oriented distance function and its application[J]. Operations Research Transactions, 2024, 28(2): 117-130.

图/表 4

参考文献 21

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定向距离函数的光滑化方法及其应用

The smoothing method of the oriented distance function and its application

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