Multiple local minima in radiotherapy optimization problems with dose–volume constraints

摘要: The cause of multiple local minima in beam weight optimization problems subject to dose–volume constraints is analyzed. Three objective functions were considered: (a) maximization tumorcontrol probability (TCP), (b) the minimum target dose, and (c) minimization mean-squared-deviation dose from prescription dose. It shown that: TCP models generally result strongly quasiconvex functions; results a function; minimizing root-mean-square deviation convex function. Dose–volume are considered such that, for each region at risk (RAR), volume tissue whose exceeds certain tolerance (D Tol ) kept equal or below given fractional level (v ). If all RARs lack “volume effect” (i.e., v =0 RARs) then there single minimum. But if effects present, feasible space possibly nonconvex therefore leads minima. These conclusions hold three functions. Hence, possible come not nonlinear nature considered, but “either this that both” effect. observations imply algorithms dose-volume constraint types should have effective strategies dealing with