Analytical Solution for the Generalized Fermat–Torricelli Problem

Alexei Yu. Uteshev
2014 The American mathematical monthly  
We present explicit analytical solution for the problem of minimization of the function F (x, y) = 3 j=1 m j (x − x j ) 2 + (y − y j ) 2 , i.e. we find the coordinates of stationary point and the corresponding critical value as functions of {m j , x j , y j } 3 j=1 . In addition, we also discuss inverse problem of finding such values for m 1 , m 2 , m 3 for which the corresponding function F possesses a prescribed position of stationary point.
doi:10.4169/amer.math.monthly.121.04.318 fatcat:dlgjhxj2wbegnja3tqiaym2u6e