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A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax−|x| = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1000-dimensional AVEs to an accuracy of 10 −6 in less than 10 seconds each. Similarly, AVEs corresponding to 100 randomly generated… (More)

Given M ∈ n×n and q ∈ n , the linear complementarity problem (LCP) is to find (x, s) ∈ n × n such that (x, s) ≥ 0, s = M x + q, x T s = 0. By using the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of… (More)

In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported.