YAM2: Yet another library for the M_2 variables using sequential quadratic programming

The M_2 variables are devised to extend M_T2 by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible particles, where the variable definitions directly provide how to calculate them, the calculation of the M_2 variables is undertaken by employing numerical algorithms. Essentially, the calculation of M_2 corresponds to solving a constrained minimization problem in mathematical optimization, and various numerical methods exist for the task. We find that the sequential quadratic programming method performs very well for the calculation of M_2, and its numerical performance is even better than the method implemented in the existing software package for M_2. As a consequence of our study, we have developed and released yet another software library, YAM2, for calculating the M_2 variables using several numerical algorithms.