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Received June 26, 2018; Accepted November 12, 2018; Published November 22, 2018
Abstract. In this paper, an infeasible path-following interior-point algorithm is proposed for solving the NP-hard absolute value equations (AVE) of the type Ax – B|x| = b. Under the condition that the minimal singular value of A is strictly greater than the maximal singular value of B, the unique solvability theorem of AVE is presented by formulating the AVE as a monotone horizontal linear complementary problem (HLCP). We also propose an infeasible primal-dual interior-point algorithm for solving the AVE across the HLCP. Some numerical results are provided to show the efficiency of the proposed algorithm.
How to Cite this Article:
Mohamed Achache, Nadia Hazzam, Solving absolute value equations via complementarity and interior-point methods, Journal of Nonlinear Functional Analysis, Vol. 2018 (2018), Article ID 39, pp. 1-10.