Smoothing Newton algorithm for symmetric cone complementarity problems based on a one-parametric class of smoothing functions
In this paper, we introduce a one-parametric class of smoothing functions in the context of symmetric cones which contains
two symmetric perturbed smoothing functions as special cases, and show that it is coercive under suitable assumptions. Based
on this class of smoothing functions, a smoothing Newton algorithm is extended to solve the complementarity problems over
symmetric cones, and it is proved that the proposed algorithm is globally and locally superlinearly convergent under suitable
assumptions. The theory of Euclidean Jordan algebras is a basic tool which is extensively used in our analysis. Preliminary
numerical results for randomly generated second-order cone programs and several practical second-order cone programs from
the DIMACS library are reported.