It turns out that it is not trivial to solve. The average of the participant locations is not necessarily the optimal point. The actual optimal point is called the geometric median.
I made a HTML5 page which visualizes the geometric median, along with the convex cost function: http://www.byronknoll.com/median.html
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAJMxuDZrFQCcFUX00pDWrAzBKM2VBxJqnnPJBbMRj8Nm9lQzqq7nhvN72NEAxwPui6_v_Iqtrn8pXfTuCscM5oq9cpqka7EdtNbotb9XZyaZEkbXV5UTEJK2vJ7AD0icsNoqL/s320/median2.png)