A Full Nesterov-Todd Step Infeasible Interior-Point Method 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 coincides with the currently best iteration bound for second-order conic optimization. We also generalize an infeasible interior-point method for linear optimization to second-order conic optimization. As usual for infeasible interior-point methods, the starting point depends on a positive number. The algorithm either finds a solution in a finite number of iterations or determines that the primal-dual problem pair has no optimal solution with vanishing duality gap. [ABSTRACT FROM AUTHOR]