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Zbl 1149.90098
Mangasarian, O.L.
Absolute value equation solution via concave minimization. (English)
[J] Optim. Lett. 1, No. 1, 3-8 (2007). ISSN 1862-4472; ISSN 1862-4480/e

Summary: The NP-hard absolute value equation (AVE) $Ax - |x| = b$ where $A\in R^{n\times n}$ and $b\in R^n$ is solved by a succession of linear programs. The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter by successive linearization. A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1,000-dimensional random instances of the AVE with only five violated equations out of a total of 100,000 equations.

MSC 2000:: *90C05 Linear programming

Keywords: absolute value equation; concave minimization; successive linear programming

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Zentralblatt MATH Berlin [Germany]