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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.

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