Kernel-Based Interior-Point Methods for Monotone LCP over Symmetric Cones

We present a generic interior-point method for monotone LCP over symmetric cones that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. Furthermore, the method uses Nesterov-Todd search directions. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. For some specific eligible kernel functions we match the best known iteration bound for large-step methods while for short-step methods the best iteration bound is matched for all cases.