Primal-dual interior-point algorithm for convex quadratic semi-definite optimization

In this paper, we present a new primal-dual interior-point algorithm for solving a special case of convex quadratic semi-definite optimization based on a parametric kernel function. 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 algorithm. These properties enable us to derive the currently best known iteration bounds for the algorithm with large- and small-update methods, namely, O(nlognlognε) and O(nlognε), respectively, which reduce the gap between the practical behavior of the algorithm and its theoretical performance results.