A kinematical constrained fit using the Lagrange multipliers method

The bundling of tracks taking into account the kinematical constraint given by the invariant mass of the mother particle and the geometrical ones of having a common point in space, is a problem which involves finding the extrema of a multivariate function subjected to a certain set of analytical constraints. In the present note I will describe in detail an algorithm, based on the Lagrange multipliers method, to perform this kind of fit. This algorithm was implemented in a set of Fortran routines to be used in the context of the LHCb analysis library. This implementation is also briefly discussed. Finally, a brief note on the K0s reconstruction is given.1