A full Nesterov-Todd step infeasible interior-point algorithm for symmetric optimization based on a specific kernel function

Abstract

We present a full Nesterov-Todd step infeasible interior-point algorithm based on a kernel function. Each main iteration of the algorithm consists of a feasibility step and some centering steps. We introduce a kernel function in the algorithm to induce the feasibility step. The iteration bound coincides with the best iteration bound for infeasible interior-point methods, that is, $O(r\log\frac{r}{\epsilon})$, where $r$ is the rank of Euclidean Jordan algebra.