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

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  • Based on the KK smoothing function, we introduce a regularized one-parametric class of smoothing functions and show that it is coercive under suitable assumptions. By making use of the introduced regularized one-parametric class of smoothing functions, we investigate a smoothing Newton algorithm for solving the generalized complementarity problems over symmetric cones (GSCCP), where a nonmonotone line search scheme is used. We show that the algorithm is globally and locally superlinearly convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool in our analysis.
    Mathematics Subject Classification: Primary: 90C22; Secondary: 90C25.

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