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12 Aug 2006
Absolute value equation solution via concave minimization
 O. L. Mangasarian
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The NPhard 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 piecewiselinear 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 1,000dimensional random instances of the AVE with only five violated equations out of a total of 100,000 equations.
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 Title
 Absolute value equation solution via concave minimization
 Journal

Optimization Letters
Volume 1, Issue 1 , pp 38
 Cover Date
 20070101
 DOI
 10.1007/s1159000600056
 Print ISSN
 18624472
 Online ISSN
 18624480
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Absolute value equation
 Concave minimization
 Successive linear programming
 Authors

 O. L. Mangasarian ^{(1)} ^{(2)}
 Author Affiliations

 1. Computer Sciences Department, University of Wisconsin, Madison, WI, 53706, USA
 2. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093, USA