On convergence of the optimization process in Radiotherapy treatment planning

TL;DR

This paper investigates the convergence behavior of a quasi-Newton optimization algorithm in radiotherapy planning, revealing potential slowdowns near critical dose values due to histogram differentiability issues.

Contribution

It provides an analysis of convergence challenges in dose-volume constrained optimization, highlighting the impact of histogram differentiability on algorithm performance.

Findings

Convergence may slow down near critical dose values.

Finite differentiability of dose-volume histograms affects optimization.

Slower convergence does not necessarily mean failure.

Abstract

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.