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.

翻译：本文研究二阶锥形(SOCP)不可行的内点方法(IPM)最差的重复复杂情况,较之于可行的静脉注射器,这种方法更便于暖动启动;该方法研究的是单一和自体模型和蒙泰罗-张氏搜索方向系列的基础;其最差的重复复杂情况是$Oleft(k ⁇ 1/2 ⁇ log\left(epsilon ⁇ -1 ⁇ right)\right),以将原始剩余、双重剩余和互补差距减少1美元,其中美元是锥形限制的数量;其结果与已知的可行静脉注射器最佳结果相同;还研究了暖起动改善复杂界限的条件。