On convergence of the optimization process in Radiotherapy treatment planning

The Radiotherapy treatment planning optimization process based on a quasi-Newton algorithm with an object function containing dose-volume constraints is not guaranteed to converge when the dose value in the dose-volume constraint is a critical value of the dose distribution. This is caused by finite differentiability of the dose-volume histogram at such values. A closer look near such values reveals that convergence is most likely not at stake, but it might be slowed down.