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Absolute value equations. (English) Zbl 1172.15302
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.

15A39Linear inequalities of matrices
Full Text: DOI
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[7] O.L. Mangasarian, Absolute value programming, Technical Report 05-04, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, WI, September 2005. Available from: <ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/05-04.ps>. Comput. Optim. Appl., in press.