Computational geometry - main stream convex optimisation?

As Tasos pointed out there's an open position in "Large Scale Convex Optimization" at University of Sydney.

For that reason I would be very interested to hear if anyone has any ideas on how one can argue that computational geometry is actually "Large Scale Convex Optimization", or even that it's remotely related to it.

Really good ideas will be awarded with beer (non-alcoholic of course).