Abstract
This paper mainly aims to obtain a minimum norm solution to the NP-hard absolute value equations (AVE) \(Ax-|x|=b\). In our proposed method, first we show that the AVE is equivalent to a bilinear programming problem and then we present a system tantamount to this problem. To find the minimum norm solution to the AVE, we solve a quadratic programming problem with quadratic and linear constraints. Eventually, we solve the obtained programming problem by Simulated Annealing algorithm. Numerical results support the efficiency of the proposed method and the high accuracy of calculation.
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