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In this paper a special piecewise linear system is studied. It is shown that,under a mild assumption, the semi-smooth Newton method applied to this systemis well defined and the method generates a sequence that converges linearly toa solution. Besides, we also show that the generated sequence is bounded, forany starting point, and a formula for any accumulation point of this sequenceis presented. As an application, we study the convex quadratic programmingproblem under positive constraints. The numerical results suggest that thesemi-smooth Newton method achieves accurate solutions to large scale problemsin few iterations.

A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming