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运筹学学报 >

2024 , Vol. 28 >Issue 2: 117 - 130

DOI: https://doi.org/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

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  • 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
高英  E-mail: gaoyingimu@163.com

收稿日期: 2022-11-01

  网络出版日期: 2024-06-07

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)

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运筹学学报编辑部, 2024, 版权所有，未经授权。
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The smoothing method of the oriented distance function and its application

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  • 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 date: 2022-11-01

  Online published: 2024-06-07

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, 2024, All rights reserved, without authorization
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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

本文引用格式

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, 2024 , 28(2) : 117 -130 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.02.009

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

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