We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc.) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraints sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

## Citation

Physics in Medicine and Biology, Vol. 51 (2006), pp. 2353-2365. Available from IOP Select (http://www.iop.org/Select/) for one year from online publication time.