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Zbl 1172.15302
Mangasarian, O.L.; Meyer, R.R.
Absolute value equations.
(English)
[J] Linear Algebra Appl. 419, No. 2-3, 359-367 (2006). ISSN 0024-3795

Summary: We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: $Ax -\vert x\vert = b$, where $A$ is an arbitrary $n\times n$ 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.
MSC 2000:
*15A39 Linear inequalities

Keywords: absolute value equations; linear complementarity problems

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