Key Notes on Fixed Point Programming in Particle Radiotherapy

The paper examines the violations of monotonicity and semiconvergence of the inverse optimization problem to equilibrium iterative solutions under conditions of physical density discontinuities in therapy planning techniques. Additionally, it addresses aspects of quasi-Newton iterations of the obtained solution in both voxel representation and continuous approximation. Examples include radiation treatment plans for patients treated with proton beam at the Prometheus therapeutic facility at the A. Tsyb Medical Radiological Research Center, Obninsk, Kaluga oblast, Russia. The presented aspects of the theory and its applications form the basis of the dose-anatomical planning program.