A successive LP approach with C-VaR type constraints for IMRT optimization

In the proposed method, we integrate the C-VaR type constraints with a successive LP approach. Exploiting the solution of LP problems, we automatically detect outliers and remove them from the domain of the C-VaR type constraints. This reduces the sensitivity of the C-VaR type constraints to outliers, therefore, we can search feasible plans in a wider region than the C-VaR type constraints. We give a mathematical proof that if the optimal value of an LP problem in the proposed method is non-positive, the corresponding optimal solution satisfies all the DVCs. From a numerical experiment on test data sets, we observed that the proposed method found feasible solutions more appropriately than existing successive LP approaches. Moreover, the proposed method required fewer LP problems, and this was reflected in a short computation time.