  Fluence map optimization for intensity-modulated radiation therapy planning
can be formulated as a large-scale inverse problem with competing objectives
and constraints associated with the tumors and organs-at-risk. Unfortunately,
clinically relevant dose-volume constraints are nonconvex, so standard
algorithms for convex problems cannot be directly applied. While prior work
focused on convex approximations for these constraints, we propose a novel
relaxation approach to handle nonconvex dose-volume constraints. We develop
efficient, provably convergent algorithms based on partial minimization, and
show how to adapt them to handle maximum-dose constraints and infeasible
problems. We demonstrate our approach using the CORT dataset, and show that it
is easily adaptable to radiation treatment planning with dose-volume
constraints for multiple tumors and organs-at-risk.
