optimization with multivariable and constraint

Hi, I have a similar problem. i want to minimize a function with multi variable and constraint. i used fmin function but i think i am making some error.

here is the problem : Let P1 = (x1, y1) and P2 =

(x2, y2) be two given points. Find the third point P3 = (x3, y3) such that

d1 = d2 is minimized, where d1 is the distance from P3 to P1 and d2 is the

distance from P3 to P2.

so objective function is d1 + d2 =0 and constraint is d1=d2

where d1 = [(x3-x1)^2 +(y3-y1)^2]^1/2 & d2= [(x3-x2)^2 +(y3-y2)^2]^1/2

can you please help

Answer 1

[John D'Errico]

Sorry, but this seems just plain silly. You are way overthinking things.

The new point P3 lies at the midpoint of the straight line segment connecting P1 and P2. So if

P1 = [x1,y1];
P2 = [x2,y2];

P3 = (P1 + P2)/2;

No optimization necessary. No constraints. No need to use a Mack truck to carry a pea to Boston.