The method of intercepts in parameter space for the analysis of local minima caused by dose-volume constraints

The local minima problem in radiotherapy optimization has been a concern for both researchers and physicians. In this work, local minima induced by dose-volume histogram (DVH) constraints are discussed. The non-convex property of the feasible set formed by DVH constraints is discussed in beam weight space. An intuitive explanation of the origin of this type of local minima is given by a two-beam model setup. Some interesting properties and insights about the DVH-induced local minima are found. Based on this, a heuristic non-random initial guess sampling method is proposed and applied to a clinical nasopharyngeal case, where some significantly different local minima are located.