A NEW POLYNOMIAL INTERIOR-POINT ALGORITHM FOR THE MONOTONE LINEAR COMPLEMENTARITY PROBLEM OVER SYMMETRIC CONES WITH FULL NT-STEPS

In this paper, we present a new polynomial interior-point algorithm for the monotone linear complementarity problem over symmetric cones by employing the framework of Euclidean Jordan algebras. At each iteration, we use only full Nesterov and Todd steps. The currently best known iteration bound for small-update method, namely, $O(\sqrt{r}\log{\frac{r}{\varepsilon}})$, is obtained, where r denotes the rank of the associated Euclidean Jordan algebra and ε the desired accuracy.