  Within the setting of intensity modulated radiation therapy (IMRT) and the
fully continuous version of IMRT called volumetric modulated radiation therapy
(VMAT), we consider the problem of matching a given fluence map as well as
possible in limited time by the use of a linear accelerator (linac) with a
multi-leaf collimator (MLC). We introduce two modeling strategies to manage the
nonconvexity and the associated local minima of this problem. The first is the
use of linear splines to model the MLC leaf positions as functions of time. The
second is a progressively controllable smooth model (instead of a step
function) of how the leaves block the fluence radiation. We propose a two part
solution: an outer loop that optimizes the dose rate pattern over time, and an
inner loop that given a dose rate pattern optimizes the leaf trajectories.
