A non-monotone regularization Newton method for the second-order cone complementarity problem

Based on the smoothing Newton method and the Tikhonov regularization method, we construct a regularization Newton method for the second-order cone complementarity problem. The method uses a non-monotone line search scheme which contains the usual monotone line search as a special case. By using the theory of Euclidean Jordan algebras, we prove that the proposed method is globally and locally quadratically convergent under suitable assumptions. Some numerical results are reported which indicate the effectiveness of the method.