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This paper studies the worst case iteration complexity of an infeasibleinterior point method (IPM) for seconder order cone programming (SOCP), whichis more convenient for warmstarting compared with feasible IPMs. The methodstudied bases on the homogeneous and self-dual model and the Monteiro-Zhangfamily of searching directions. Its worst case iteration complexity is$O\left(k^{1/2}\log\left(\epsilon^{-1}\right)\right)$, to reduce the primalresidual, 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 bestknown result for feasible IPMs. The condition under which warmstarting improvesthe complexity bound is also studied.

Iteration Complexity of an Infeasible Interior Point Methods for Seconder-order Cone Programming and its Warmstarting