A class of polynomial interior-point algorithms for the Cartesian P∗(κ)P∗(κ) second-order cone linear complementarity problem

In this paper a class of polynomial interior-point algorithms for the Cartesian P∗(κ)P∗(κ) second-order cone linear complementarity problem based on a parametric kernel function, with parameters p∈[0,1]p∈[0,1] and q≥1q≥1, are presented. The proposed parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and the μμ-center for the algorithms. Moreover, the currently best known iteration bounds for the large- and small-update methods, namely, O((1+2κ)NlogNlogNε) and O((1+2κ)NlogNε), are obtained, respectively, which reduce the gap between the practical behavior of the algorithms and its theoretical performance results.