Solving k-center problems involving sets based on optimization techniques

被引：84
|
作者：
Nguyen Thai An [2 ,3 ]
Nguyen Mau Nam [4 ]
Qin, Xiaolong [1 ,2 ,5 ]
机构：
[1] Hangzhou Normal Univ, Dept Math, Hangzhou, Zhejiang, Peoples R China
[2] Univ Elect Sci & Technol China, Inst Fundamental & Frontier Sci, Chengdu 611731, Sichuan, Peoples R China
[3] Duy Tan Univ, Inst Res & Dev, Da Nang, Vietnam
[4] Portland State Univ, Fariborz Maseeh Dept Math & Stat, Portland, OR 97207 USA
[5] Zhejiang Normal Univ, Dept Math, Jinhua, Zhejiang, Peoples R China
来源：
JOURNAL OF GLOBAL OPTIMIZATION | 2020年 / 76卷 / 01期
基金：
中国博士后科学基金; 中国国家自然科学基金; 美国国家科学基金会;
关键词：
k-center problem; Multifacility location problem; Majorization-minimization principle; Difference of convex functions; SMALLEST ENCLOSING BALL; FACILITY LOCATION; EFFICIENT ALGORITHMS; MINIMAX;
D O I：
10.1007/s10898-019-00834-6
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The continuous k-center problem aims at finding k balls with the smallest radius to cover a finite number of given points in R-n. In this paper, we propose and study the following generalized version of the k-center problem: Given a finite number of nonempty closed convex sets in R-n, find k balls with the smallest radius such that their union intersects all of the sets. Because of its nonsmoothness and nonconvexity, this problem is very challenging. Based on nonsmooth optimization techniques, we first derive some qualitative properties of the problem and then propose new algorithms to solve the problem. Numerical experiments are also provided to show the effectiveness of the proposed algorithms.
引用
收藏
页码：189 / 209
页数：21
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