  Interior point methods solve small to medium sized problems to high accuracy
in a reasonable amount of time. However, for larger problems as well as
stochastic problems, one needs to use first-order methods such as stochastic
gradient descent (SGD), the alternating direction method of multipliers (ADMM),
and conjugate gradient (CG) in order to attain a modest accuracy in a
reasonable number of iterations. In this report, we first discuss heuristics
for diagonal scaling. Next, we motivate preconditioning by an example, and then
we study preconditioning for a specific splitting form in ADMM called graph
projection splitting. Finally we examine the performance of our methods by some
numerical examples.
