Absolute value equations

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We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax - {divides}x{divides} = b, where A is an arbitrary n × n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments. © 2006 Elsevier Inc. All rights reserved.




Mangasarian, O. L., & Meyer, R. R. (2006). Absolute value equations. Linear Algebra and Its Applications, 419(2–3), 359–367. https://doi.org/10.1016/j.laa.2006.05.004

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