# Inexact Newton method for minimization of convex piecewise quadratic functions

## TL;DR

This paper introduces an inexact Newton method tailored for minimizing convex piecewise quadratic functions, with proven convergence and practical applications in linear algebra and computational geometry.

## Contribution

It presents a novel inexact Newton algorithm for convex piecewise quadratic functions, extending its application to linear systems and polyhedral distance problems.

## Key findings

- Method successfully applied to large sparse matrices.
- Convergence analysis confirms theoretical robustness.
- Effective in practical computational geometry tasks.

## Abstract

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.