Inexact Newton Method for Minimization of Convex Piecewise Quadratic Functions
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 optimization 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.
This work was partially supported by the Russian Foundation for Basic Research grant No. 17-07-00510. The authors are grateful to the anonymous referees and to Prof. V. Garanzha for many useful comments which greatly improved the exposition of the paper.
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