Efficient schemes for robust IMRT treatment planning.

We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and interfraction positional uncertainty of tumour and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and efficient approach for solving this problem, and present results to compare the performance of our scheme with more conventional formulations that assume perfect knowledge of the dose matrix.