A Characterization of the Fermat Point in Hilbert Spaces

被引：0
作者：
Diana–Olimpia Alexandrescu
机构：
[1] University of Craiova,Department of Mathematics
来源：
Mediterranean Journal of Mathematics | 2013年 / 10卷
关键词：
Primary 49K35; Fermat point; Hilbert space; close form formula; space with positive measure; iterative method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper studies the Fermat point in Hilbert spaces for a system of n distinct points. We prove the existence of the Fermat point and we determine its location in the convex hull of the given system of points. A new concept of Fermat point for a non–discrete set of points is introduced and there are proved similar results to discrete case. In the second part of this paper we give close form formulas of Fermat point for a system of 3 and 4 distinct points. We also describe some iterative methods to find the Fermat point for a system of more than 4 distinct points.
引用
收藏
页码：1509 / 1525
页数：16
相关论文
共 28 条
[1]  
Dalla L.(2001)A note on the Fermat–Torricelli point of a d–Simplex J. Geom. 70 38-43
[2]  
Dalla L.(2002)The blocking numbers of convex bodies Discrete Comput. Geom. 24 267-277
[3]  
Larman D. G.(2003)Geometrical solution to the Fermat problem with arbitrary weights Ann. Oper. Res. 123 67-104
[4]  
Mani–Levitska P.(1997)On the Torricelli’s geometrical solution to a problem of Fermat Duality in practice. IMA J. Math. Appl. Bus. Indust. 8 215-224
[5]  
Zong C.(1973)A note on Fermat’s problem Math. Program. 4 98-107
[6]  
Jalal G.(1994)The Fermat–Torricelli point and the isosceles thetraedra J. Geom. 49 150-162
[7]  
Krarup J.(1998)Convergence properties of the Nelder–Mead simplex method in low dimensions SIAM J. Optim. 9 112-147
[8]  
Krarup J.(2002)The Fermat–Torricelli problem in normed planes and spaces J. Optim. Theory Appl. 115 283-314
[9]  
Vajda S.(1999)Convergence of the Nelder–Mead simplex method to a nonstationary point SIAM J. Optim. 9 148-158
[10]  
Kuhn H.(2011)Applications of variational analysis to a generalized Fermat–Torricelli problem J. Optim. Theory Appl. 148 431-454
123