Interesting approach but I feel it lacks some robustness since reciprocal mentions do not always correlate with similar spatial location. Further the optimisation seems rather heuristic. I would suggest adopting LADMPSAP for the optimisation.
Their approach minimises the total variation of the geographic location for each person with other the people for which there they have reciprocal mentions. Essentially it's minimising the sum_k of abs(l_i - l_k) where l_i is the location of a particular person and l_k is a "friend". If the members of l_k are spread out geographically around the world you will get poor location accuracy. This is what I mean by not being robust.
As for optimisation: I only read the paper quickly and didn't really see as you formal proof of convergence for their optimisation approach. They should use a scheme which is known to be globally convergent such as LADMPSAP.
