A modified SOR-like method for absolute value equations associated with second order cones

In this paper, we propose a modified SOR-like method for solving absolute value equations associated with second order cones (SOCAVE in short), which is obtained by reformulating the SOCAVE as a two-by-two block nonlinear equation. The convergence analysis and error estimation of this method are established under mild assumptions on system matrix and iteration parameters. And, the optimal iteration parameters and the corresponding optimal convergence factor are studied. In particular, we present the approximate optimal iteration parameters which are independent of the number of iterations. Numerical results are given to show the efficiency of the proposed iteration method with suitable parameters. (C) 2021 Elsevier B.V. All rights reserved.