  We discuss quantum optimal control of Bose-Einstein condensates trapped in
magnetic microtraps. The objective is to transfer a condensate from the ground
state to the first-excited state. This type of control problem is typically
solved using derivative-based methods in a high-dimensional control space such
as gradient-ascent pulse engineering (GRAPE) and Krotov's method or
derivative-free methods in a reduced control space such as Nelder-Mead with a
chopped random basis (CRAB). We discuss how these methods can be combined in
gradient optimization using parametrization (GROUP) including the finite
bandwidth of the control electronics. We compare these methods and find that
GROUP converges much faster than Nelder-Mead with CRAB and achieves better
results than GRAPE and Krotov's method on the control problem presented here.
