New complexity analysis of interior - point methods for the Cartesian P ∗ ( κ ) - SCLCP

In this paper, we give a unified analysis for both largeand small-update interior-point methods for the Cartesian P∗(κ )-linear complementarity problem over symmetric cones based on a finite barrier. The proposed finite barrier is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the algorithm. The symmetry of the resulting search directions is forced by using the Nesterov-Todd scaling scheme. By means of Euclidean Jordan algebras, together with the feature of the finite kernel function, we derive the iteration bounds that match the currently best known iteration bounds for largeand small-update methods. Furthermore, our algorithm and its polynomial iteration complexity analysis provide a unified treatment for a class of primal-dual interior-point methods and their complexity analysis. MSC: 90C33; 90C51