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Operations Research Transactions >

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

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.02.009

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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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

Cite this article

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

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