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arXiv · 1508.01582

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

J. G. Barrios·J. Y. Bello Cruz·O. P. Ferreira·S. Z. Németh
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Abstract

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 system is well defined and the method generates a sequence that converges linearly to a solution. Besides, we also show that the generated sequence is bounded, for any starting point, and a formula for any accumulation point of this sequence is presented. As an application, we study the convex quadratic programming problem under positive constraints. The numerical results suggest that the semi-smooth Newton method achieves accurate solutions to large scale problems in few iterations.

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J. G. Barrios, J. Y. Bello Cruz, O. P. Ferreira, S. Z. Németh. 2015-08-07. A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming. https://arxiv.org/abs/1508.01582

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