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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)
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.
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)