A Primal-Dual Interior-Point Algorithm for Convex Quadratic Optimization Based on a Parametric Kernel Function

In this paper a primal-dual interior-point algorithm for convex quadratic optimization based on a parametric kernel function, with parameters p isin [0,1] and q ges 1, is presented. The proposed parametric kernel function is of excellent properties which are used both for determining the search directions and measuring the distance between the given iterate and the central path for the algorithm. These properties enable us to derive the currently best known iteration bound for the algorithm with large-update method, namely, O(radicn log n log n/isin), which reduces the gap between the practical behavior of the algorithm and its theoretical performance results.