For MAP, MCE and MCE-F, we used the L 2norm regularization.
it has been shown (Le Roux and McDer-mott, 2005) that even simple gradient-based (firstorder) optimization methods such as GPD and (approximated) second-order methods such as Quick-Prop (Fahlman, 1988) and BFGS-based methods have yielded good experimental optimization results.