  This paper studies the worst case iteration complexity of an infeasible
interior point method (IPM) for seconder order cone programming (SOCP), which
is more convenient for warmstarting compared with feasible IPMs. The method
studied bases on the homogeneous and self-dual model and the Monteiro-Zhang
family of searching directions. Its worst case iteration complexity is
$O\left(k^{1/2}\log\left(\epsilon^{-1}\right)\right)$, to reduce the primal
residual, dual residual, and complementarity gap by a factor of $\epsilon$,
where $k$ is the number of cone constraints. The result is the same as the best
known result for feasible IPMs. The condition under which warmstarting improves
the complexity bound is also studied.
