Given the wide range of optimization methods, which is the appropriate method to use? I am thinking of using either linear programming (interior-point methods) or augmented Lagrangian methods. Which method will be more approriate for large scale linear problem with equality constraint? Thank you.
I would recommend you to grab a copy of matlab as many linear programming algorithms are implemented and you can directly compare how they perform on your data.
However it should also be a good hint to see what they use for your problem: