A Large-update Interior-point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function

In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O( n1/2(log n)2 log n/c ). This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and recent kernel functions introduced by some authors in optimization fields. Some computational results have been provided.