Kernel‐Based Interior‐Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones

We present an interior‐point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class is fairly general and includes the classical logarithmic function, the self‐regular functions, as well as many non‐self‐regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both large‐step and short‐step versions of the method for ten frequently used eligible kernel functions. For some of them 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. The paper generalizes results of Lesaja and Roos (2010) from P *(κ)‐LCP over the non‐negative orthant to monotone LCPs over symmetric cones.