OCNov 12, 2015
On the global convergence of the inexact semi-smooth Newton method for absolute value equationJ. Y. Bello Cruz, O. P. Ferreira, L. F. Prudente
In this paper, we investigate global convergence properties of the inexact nonsmooth Newton method for solving the system of absolute value equations (AVE). Global $Q$-linear convergence is established under suitable assumptions. Moreover, we present some numerical experiments designed to investigate the practical viability of the proposed scheme.
OCNov 12, 2015
A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programmingJ. G. Barrios, J. Y. Bello Cruz, O. P. Ferreira et al.
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.