Algorithm to find point of minimum total distance from locations

Question

I\'m building an application based around finding a \"convenient meeting point\" given a set of locations.

Currently I\'m defining \"convenient\" as \"minimising the

Answer 1

In a way what you appear to be looking for is the center of mass of a triangle with equal weights at the vertices. That would point to barycentric coordinates.

When going beyond a triangle there are solutions for generalized barycentric coordinates and you could give priorities to persons by modifying the weight of the vertices. What that still would not account for is distances on a real map (can't just travel straight in any direction) but it may be a start?