  A fast and stable algorithm for estimating multidimensional adaptive P-spline
models is presented. We call it as Separation of Overlapping Penalties (SOP) as
it is an extension of the \textit{Separation of Anisotropic Penalties} (SAP)
algorithm. SAP was originally derived for the estimation of the smoothing
parameters of a multidimensional tensor product P-spline model with anisotropic
penalties.
