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Journal of Optimization Theory and Applications

, Volume 146, Issue 3, pp 735–744 | Cite as

An Extension of the Fermat-Torricelli Problem

  • T. V. Tan
Article

Abstract

The Fermat-Torricelli problem is an optimization problem associated with a finite subset \(\{a_{j}\}_{j=1}^{q}\) of ℝ N and a family \(\{c_{j}\}_{j=1}^{q}\) of positive weights. The function F to be minimized is defined by \(F(x)=\sum _{j=1}^{q}c_{j}\Vert x-a_{j}\Vert\). In this paper, we extend this problem to the case of volumes.

Keywords

Fermat-Torricelli problem Weber problem Finite-dimensional space 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam

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