Local solutions of the multi-source Weber problem

Several new qualitative properties of the problem of minimizing the sum of the weighted minima of the Euclidean distances of the demand points to the facilities, which is called the multi-source Weber problem and also known as the clustering problem with Euclidean norms, are obtained in this paper....

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Published inOptimization Vol. 74; no. 8; pp. 1899 - 1913
Main Authors Cuong, Tran Hung, Wen, Ching-Feng, Yao, Jen-Chih, Yen, Nguyen Dong
Format Journal Article
LanguageEnglish
Published Taylor & Francis 11.06.2025
Subjects
DC programming
local solutions
Multi-source Weber problem
optimality condition
subdifferential of a convex function
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Abstract Several new qualitative properties of the problem of minimizing the sum of the weighted minima of the Euclidean distances of the demand points to the facilities, which is called the multi-source Weber problem and also known as the clustering problem with Euclidean norms, are obtained in this paper. Nontrivial local solutions are defined and characterized with the help of a necessary optimality condition in DC programming and the special structure of the problem in question. Since most of the existing solution algorithms for this problem just give some local solutions, our characterizations can be used to analyse and refine these algorithms.
AbstractList Several new qualitative properties of the problem of minimizing the sum of the weighted minima of the Euclidean distances of the demand points to the facilities, which is called the multi-source Weber problem and also known as the clustering problem with Euclidean norms, are obtained in this paper. Nontrivial local solutions are defined and characterized with the help of a necessary optimality condition in DC programming and the special structure of the problem in question. Since most of the existing solution algorithms for this problem just give some local solutions, our characterizations can be used to analyse and refine these algorithms.
Author Cuong, Tran Hung
Yen, Nguyen Dong
Wen, Ching-Feng
Yao, Jen-Chih
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Snippet Several new qualitative properties of the problem of minimizing the sum of the weighted minima of the Euclidean distances of the demand points to the...
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StartPage 1899
SubjectTerms DC programming
local solutions
Multi-source Weber problem
optimality condition
subdifferential of a convex function
Title Local solutions of the multi-source Weber problem
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