title: Algorithm to find point of minimum total distance from locations
body: <p>I'm building an application based around finding a "convenient meeting point" given a set of locations.</p>
  
  <p>Currently I'm defining "convenient" as "minimising the total travel distance". This is a different problem from finding the centroid as illustrated by the following example (using cartesian coordinates rather than latitude and longitude for convenience):</p>
  
  <ul>
  <li>A is at (0,0)</li>
  <li>B is at (0,0)</li>
  <li>C is at (0,12)</li>
  </ul>
  
  <p>The location of minimum total travel for these points is at (0,0) with total travel distance of 12; the centroid is at (0,4) with total travel distance of 16 (4 + 4 + 8).</p>
  
  <p>If the location were confined to being at one of the points, the problem appears to become simpler, but this isn't a constraint I intend to have (unlike, for example, <a href="https://stackoverflow.com/questions/7171011/minimum-sum-of-all-travel-times">this otherwise similar question</a>).</p>
  
  <p>What I can't seem to do is come up with any sort of algorithm to solve this - suggestions welcomed please!</p>