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Updated: Aug 15, 2025
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Radiation Planning Assistant - A Streamlined, Fully Automated Radiotherapy Treatment Planning System
Published on: April 11, 2018
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Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising
Mark Brooke1, Yair Censor2, Aviv Gibali3
1Department of Oncology University of Oxford Oxford OX3 7DQ UK.
International Transactions in Operational Research : a Journal of the International Federation of Operational Research Societies
|December 30, 2022
Summary
We introduce percentage violation constraints (PVCs) for optimization problems. Our new method applies these to radiation therapy treatment planning, improving feasibility-seeking methods.
Area of Science:
- Optimization Theory
- Medical Physics
- Computational Science
Background:
- Optimization problems often involve complex constraints.
- Radiation therapy treatment planning (RTTP) presents unique feasibility challenges.
- Existing methods may struggle with the nonconvexity introduced by certain constraints.
Purpose of the Study:
- To develop a novel method for solving feasibility problems with percentage violation constraints (PVCs).
- To adapt these methods for radiation therapy treatment planning (RTTP).
- To analyze the theoretical underpinnings and practical application of the proposed algorithm.
Main Methods:
- Formulating a split feasibility problem with PVCs.
- Developing a string-averaging CQ-method using projections onto half-spaces.
- Applying the CQ algorithm by Byrne (2002) to the specific problem structure.
Main Results:
- A novel CQ-method is proposed for feasibility problems with PVCs.
- The method utilizes projections onto half-spaces, simplifying computations.
- The approach is demonstrated to be applicable to RTTP, with a numerical example provided.
Conclusions:
- The developed string-averaging CQ-method offers a viable approach for feasibility problems with PVCs.
- This method shows promise for improving radiation therapy treatment planning.
- Further research is needed to extend the results to nonconvex sets.
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