A method optimizes a dose of radiation for a radio-therapy treatment subject to constraints on diagnostic parameters of the radio-therapy treatment. The method determines a point of a polytope arranged in a coordinate system of the diagnostic parameters, such that a position of the point in the coordinate system is determined at least in part by values of each diagnostic parameter. The polytope is convex with boundaries formed by intersecting half-spaces of feasible values of each diagnostic parameter specified by the constraints. The point is the closest point of the polytope to an origin of the coordinate system with regard to a weighted Euclidean distance norm. The method determines a distribution of the dose of radiation for the radio-therapy treatment using the values of the diagnostic parameters corresponding to the position of the point.
