Guaranteed [Formula: see text]-optimal solutions with the linear optimizer ART3+O.

Area of Science:

• Medical Physics
• Computational Biology
• Radiation Oncology

Background:

• The ART3+O algorithm efficiently solves large-scale inverse planning problems in radiation therapy using iterative projection.
• A key limitation of ART3+O is its inability to guarantee optimality due to an arbitrary stopping criterion.

Purpose of the Study:

• To enhance the ART3+O algorithm by introducing a novel stopping criterion.
• To ensure the algorithm finds an optimal solution in finite time for radiation therapy inverse planning.

Main Methods:

• The improved algorithm incorporates Farkas' lemma to establish a theoretically grounded stopping criterion.
• Farkas' lemma is also utilized for detecting inconsistencies in other projection-based methods.
• The enhanced algorithm's performance is validated through numerical examples in radiation therapy.

Main Results:

• The proposed modification to ART3+O guarantees the attainment of an optimal solution.
• The new stopping criterion ensures convergence in finite time.
• The method demonstrates effectiveness on radiation therapy inverse planning problems.

Conclusions:

• The modified ART3+O algorithm, utilizing Farkas' lemma, provides a robust and optimal solution for radiation therapy inverse planning.
• This approach addresses the limitations of previous methods by ensuring optimality and finite-time convergence.
• The technique offers a significant advancement in computational methods for radiation oncology.