SOLVING ABSOLUTE VALUE EQUATIONS VIA COMPLEMENTARITY AND INTERIOR-POINT METHODS

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 vertical bar x vertical bar = 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.