Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning.

We study a feasibility-seeking problem with percentage violation constraints (PVCs). These are additional constraints that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a specified fraction of the number of constraints in each subset is allowed to be violated by up to a specified percentage of the existing bounds. Our motivation to investigate problems with PVCs comes from the field of radiation therapy treatment planning (RTTP) wherein the fully discretized inverse planning problem is formulated as a split feasibility problem and the PVCs give rise to nonconvex constraints.