Original Paper

Optimization Letters

, Volume 1, Issue 1, pp 3-8

First online:

Absolute value equation solution via concave minimization

  • O. L. MangasarianAffiliated withComputer Sciences Department, University of WisconsinDepartment of Mathematics, University of California at San Diego Email author 

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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.


Absolute value equation Concave minimization Successive linear programming