A class of polynomial interior-point algorithms for the Cartesian [formula omitted] second-order cone linear complementarity problem

Abstract

In this paper a class of polynomial interior-point algorithms for the Cartesian P ∗ ( κ ) second-order cone linear complementarity problem based on a parametric kernel function, with parameters p ∈ [ 0 , 1 ] and q ≥ 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 μ -center for the algorithms. Moreover, the currently best known iteration bounds for the large- and small-update methods, namely, O ( ( 1 + 2 κ ) N log N log N ε ) and O ( ( 1 + 2 κ ) N log N ε ) , are obtained, respectively, which reduce the gap between the practical behavior of the algorithms and its theoretical performance results.