A modified smoothing and regularized Newton method for monotone second-order cone complementarity problems

In this paper, we propose a globally and quadratically convergent Newton-type algorithm for solving monotone second-order cone complementarity problems (denoted by SOCCPs). This algorithm is based on smoothing and regularization techniques by incorporating smoothing Newton’s method. Many Newton-type methods with smoothing and regularization techniques have been studied for solving nonlinear complementarity problems (NCPs) and box constrained variational inequalities (BVIs). Our algorithm is regarded as an extension of those methods to SOCCP. However, it is different from the existing methods, because we solve SOCCP by treating both the smoothing parameter μ and the regularization parameter ε as independent variables. In addition, numerical experiments indicate that the proposed method is quite effective.