Full Nesterov-Todd Step Primal-Dual Interior-Point Methods for Second-Order Cone Optimization
After a brief introduction to Jordan algebras, we present a primal-dual interior-point algorithm for second-order conic optimization that uses full Nesterov-Todd-steps; no line searches are required. The number of iterations of the algorithm is $O(\sqrt{N}\log ({N}/{\varepsilon})$, where $N$ stands for the number of second-order cones in the problem formulation and $\varepsilon$ is the desired accuracy. … Read more