Smoothing Newton algorithm based on a regularized one-parametric class of smoothing functions for generalized complementarity problems over symmetric cones

Abstract

Based on the KK smoothing function, we introduce a regularizedone-parametric class of smoothing functions and show that it iscoercive under suitable assumptions. By making use of the introducedregularized one-parametric class of smoothing functions, weinvestigate a smoothing Newton algorithm for solving the generalizedcomplementarity problems over symmetric cones (GSCCP), where anonmonotone line search scheme is used. We show that the algorithmis globally and locally superlinearly convergent under suitableassumptions. The theory of Euclidean Jordan algebras is a basic toolin our analysis.