Predictor-corrector inexact smoothing algorithm for symmetric cone complementarity problems with Cartesian P0-property

In this paper we consider the symmetric cone complementarity problem with Cartesian P-0-property (denoted by P-0-SCCP) which includes the well-known monotone symmetric cone complementarity problem. We propose a predictor-corrector inexact smoothing algorithm for solving the P-0-SCCP and prove that the method is globally and locally quadratically convergent under suitable assumptions. Especially, we prove that our algorithm can generate a bounded iteration sequence when the solution set of the P-0-SCCP is nonempty and bounded, or the solution set of the monotone SCCP is nonempty. Moreover, the proposed algorithm solves the linear systems in both predictor step and corrector step only approximately by using an inexact Newton method. Hence when one solves large-scale SCCPs, our algorithm can save much computation work compared to existing smoothing-type algorithms. Numerical results confirm these good theoretical properties. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.