Comprehensive Analysis of Kernel-Based Interior-Point Methods for P_* (κ) - LCP

We present an interior-point algorithm for P∗(κ)-linear complementarity problems, based on a barrier function defined by a new class of univariate kernel functions, called standard kernel functions (SKFs). A comprehensive and unified complexity analysis of the algorithm is provided, and a general procedure is developed to determine the iteration bounds for long-step and short-step versions of the method for the entire class of SKFs. We illustrate the general procedure by determining the iteration bounds for several parametric SKFs, which include, as special cases, all eligible kernel functions from the literature that have rational or exponential barrier terms. In all cases, we match the best iteration bounds obtained in the literature for these special cases of SKFs.