Guaranteed $\epsilon$-optimal solutions with the linear optimizer ART3+O

TL;DR

This paper improves the ART3+O linear optimizer for radiation therapy by introducing a stopping criterion based on Farkas' lemma, ensuring guaranteed epsilon-optimal solutions in finite time.

Contribution

It proposes a novel stopping criterion for ART3+O that guarantees epsilon-optimality and can detect inconsistency in projection methods.

Findings

Guarantees epsilon-optimal solutions in finite time.

Demonstrates effectiveness on radiation therapy examples.

Detects inconsistency in projection methods.

Abstract

The linear optimization algorithm ART3+O introduced by Chen et al. (2010) can efficiently solve large scale inverse planning problems encountered in radiation therapy by iterative projection. Its major weakness is that it cannot guarantee ${\epsilon}$-optimality of the final solution due to an arbitrary stopping criterion. We propose an improvement to ART3+O where the stopping criterion is based on Farkas' lemma. The same theory can be used to detect inconsistency in other projection methods as well. The proposed algorithm guarantees to find an ${\epsilon}$-optimal solution in finite time. The algorithm is demonstrated on numerical examples in radiation therapy.