Optimization Letters

, Volume 1, Issue 1, pp 3–8

Absolute value equation solution via concave minimization

Authors

    • Computer Sciences DepartmentUniversity of Wisconsin
    • Department of MathematicsUniversity of California at San Diego
Original Paper

DOI: 10.1007/s11590-006-0005-6

Cite this article as:
Mangasarian, O.L. Optimization Letters (2007) 1: 3. doi:10.1007/s11590-006-0005-6

Abstract

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.

Keywords

Absolute value equationConcave minimizationSuccessive linear programming
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© Springer-Verlag 2006