A primal-dual interior-point algorithm for absolute value equation based on a novel parametric kernel function

In this work, we provide a primal-dual interior point algorithm based on a novel parametric kernel function for the absolute value equation Ay − |y| = b. We may describe the NP-hard absolute value equation as a monotone linear complementarity problem when the singular values of the matrix A are greater than 1, demonstrating that the previous assumption guarantees the existence and uniqueness of the solution to the monotone linear complementarity problem, which is equivalent to the existence and uniqueness of the solution to the absolute value equation. The new algorithm has the best known iteration for large- and small-update methods with a given value of its parameter p. Finally, we provide some numerical results to clarify the usefulness of the suggested algorithm.