[en] Three published inverse treatment planning algorithms for physical optimization of external beam radiotherapy are compared. All three algorithms attempt to minimize a quadratic objective function of the dose distribution. It is shown that the algorithms are based on the common framework of Newton's method of multi-dimensional function minimization. The approximations used within this framework to obtain the different algorithms are described. It is shown that the two different implementations produce similar results for the simple optimization problem of conforming dose to a convex target shape. Complex optimization problems consisting of non-convex target shapes and dose limiting structures are shown to require a pencil beam optimization method. (author)