A New Full Nesterov-Todd Step Primal-Dual Path-Following Interior-Point Algorithm for Symmetric Optimization

In this paper, we generalize a primal-dual path-following interior-point algorithm for linear optimization to symmetric optimization by using Euclidean Jordan algebras. The proposed algorithm is based on a new technique for finding the search directions and the strategy of the central path. At each iteration, we use only full Nesterov-Todd steps. Moreover, we derive the currently best known iteration bound for the small-update method. This unifies the analysis for linear, second-order cone, and semidefinite optimizations.