A primal-dual interior point algorithm for convex quadratic programming based on a new kernel function with an exponential barrier term

Abstract

The introduction of kernel function in primal-dual interior point meth- ods represents not only a measure of the distance between the iterate and the central path, but also plays an important role in the amelioration of the computational complexity of an interior point algorithm. In this paper, we present a polynomial primal-dual interior-point algorithm for solving convex quadratic programming based on a new kernel function with an exponential barrier term. It is shown that in the interior-point methods based on this function, the iteration bound enjoys O( p p3n (log pn)2 log n ) and O( p p3n log n ) for large and small-update methods respectively. This complexity generalizes the result obtained by Bai et al. and improves the results obtained by Boua a et al..