The Fermat-Torricelli Problem, Part I: A Discrete Gradient-Method Approach

被引：11
|
作者：
Kupitz, Yaakov S. [1 ]
Martini, Horst [2 ]
Spirova, Margarita [2 ]
机构：
[1] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel
[2] Univ Technol, Fac Math, D-09107 Chemnitz, Germany
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2013年 / 158卷 / 02期
关键词：
Affine flats; Cauchy-Schwarz inequality; Discrete gradient method; Fasbender duality; Fermat-Torricelli problem; Location science; Multifocal ellipses; Steiner minimal trees; Steiner-Weber problem; Varignon frame; SPACES; OPTIMIZATION;
D O I：
10.1007/s10957-013-0266-z
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：
We give a discrete geometric (differential-free) proof of the theorem underlying the solution of the well known Fermat-Torricelli problem, referring to the unique point having minimal distance sum to a given finite set of non-collinear points in d-dimensional space. Further on, we extend this problem to the case that one of the given points is replaced by an affine flat, and we give also a partial result for the case where all given points are replaced by affine flats (of various dimensions), with illustrative applications of these theorems.
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页码：305 / 327
页数：23
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