  A magnitude-least-squares radiofrequency pulse design algorithm is reported
which uses interleaved exact and stochastically-generated inexact updates to
escape local minima and find low-cost solutions. Inexact updates are performed
using a small randomly selected minibatch of the available B1+ measurements to
update RF pulse weights, which perturbs the sequence of alternating
projections. Applications to RF shimming, parallel transmit spokes RF pulse
design, and spectral-spatial RF pulse design are considered. Numerical and
simulation studies characterized the optimal minibatch size, which was found to
consistently produce lower power and lower RMSE solutions across subjects, coil
geometries, B1+ resolutions and orientations. The method was validated in-vivo
at 7 Tesla and produced improvements in image quality in a slice-by-slice
RF-shimmed imaging sequence. Compared to conventional methods, the pulse design
method can more robustly design RF pulses that correct for B1+ inhomogeneities
at ultra-high field strengths, and enable pulse designs to be completed with
increased computational efficiency
