Sign controlled solvers for the absolute value equation with an application to support vector machines

2017/07/28 by Lutz Lehmann, Manuel Radons, Lehmann, Lutz +5
Computer Science · Engineering · #15A39 #62H30 #65F30 #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1707.09174

openalex publication_date 2017/07/28 · openalex created_date 2017/08/08 · openalex updated_date 2026/07/28

Abstract

Let A be a real n× n matrix and z,b∈ \mathbb Rⁿ. The piecewise linear equation system z-A\vert z\vert = b is called an absolute value equation. It is equivalent to the general linear complementarity problem, and thus NP hard in general. Concerning the latter problem, three solvers are presented: One direct, one semi-iterative and one discrete variant of damped Newton. Their previously proved ranges of correctness and convergence, respectively, are extended. Their performance is compared on instances of the XOR separation problem for support vector machines which can be reformulated as an absolute value equation.

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