Complexity Analysis of an Interior-point Algorithm for CQP Based on a New Parametric Kernel Function

Abstract

In this paper, we present a primal-dual interior-point algorithm for convex quadratic programming problem based on a new parametric kernel function with a hyperbolic-logarithmic barrier term. Using the proposed kernel function we show some basic properties that are essential to study the complexity analysis of the correspondent algorithm which we find coincides with the best know iteration bounds for the large-update method, namely, $O\left(\sqrt{n} \log n \log\frac{n}{\varepsilon}\right)$ by a special choice of the parameter $p>1$.