For what Professor Stark talked about today, if it is possible to set up constraints for the objective function (the summation Here) and have the constraints in standard form with slack variables, then we can use the Nelder Mead Simplex algorithm here.
We can do this if we find some way to iteratively linearize a sub m in the function that Stark presented on the board. Though I don't really understand what he is talking about, perhaps someone could explain this?