Analytical Solution for the Generalized Fermat-Torricelli Problem
Abstract
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 of
F(x,y)
as functions of
m
j
,
x
j
,
y
j
3
j=1
. In addition, we also discuss inverse problem of finding such values of
m
1
,
m
2
,
m
3
with the aim for the corresponding function
F
to posses a prescribed position of stationary point.