An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical grid generation... The method can be applied for computing a minimum norm nonnegative solution of underdetermined system of linear equations or for finding the distance between two convex polyhedra. The performance of the method is tested using sample data from NETLIB family of the University of Florida sparse matrix collection as well as quasirandom data. (read more)