A Predictor-Corrector Path-Following Algorithm for Symmetric Optimization Based on Darvay's Technique

Behrouz Kheirfam

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is $ \mathcal{O}(\sqrt{r} \log \dfrac{r \mu ^0}{\varepsilon})$, where $r$ is the rank of Euclidean Jordan algebra.