Abstract
By utilizing a dual complementarity condition, we propose an iterative method for solving the NP-hard absolute value equation (AVE): Ax − |x| = b, where A is an n × n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving a succession of linear programs. The algorithm was tested on 500 consecutively generated random solvable instances of the AVE with n = 10, 50, 100, 500 and 1,000. The algorithm solved 90.2 % of the test problems to an accuracy of 10−8.
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