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Absolute value equation solution via concave minimization. (English) Zbl 1149.90098
Summary: The NP-hard absolute value equation (AVE) Ax-|x|=b where AR n×n and bR 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.
90C05Linear programming
CPLEX; Matlab
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