New complexity analysis of full Nesterov-Todd step infeasible interior-point method for second-order cone optimization

Abstract

We present a full Nesterov-Todd (NT) step infeasible interior-point
algorithm for second-order cone optimization based on an adaptive of
search directions. In each iteration of the algorithm we use the
largest possible barrier parameter value $\theta$. The value
$\theta$ varies from iteration to iteration and it lies between the
two values $\frac{1}{7N}$ and $\frac{1}{6.2N}$. Moreover, Each main
iteration of the algorithm consists of a feasibility step and some
centering steps, which the feasibility step differs from the
feasibility step of the existing methods. We derive the complexity
bound which coincides with the best known bound for infeasible
interior point methods.