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An inexact Newton type method for numerical minimization of convex piecewisequadratic functions is considered and its convergence is analyzed. Earlier, asimilar method was successfully applied to optimizaton problems arising innumerical grid generation. The method can be applied for computing a minimumnorm nonnegative solution of underdetermined system of linear equations or forfinding the distance between two convex polyhedra. The performance of themethod is tested using sample data from NETLIB family of the University ofFlorida sparse matrix collection as well as quasirandom data.

Inexact Newton method for minimization of convex piecewise quadratic functions