Iri’s polynomiality proof for the Iri-Imai method recast

In a recent paper Iri showed that the Iri{Imai method converges in O(nL) iterations to an optimal solution. This is achieved by proving that in each iteration the (multiplicative) barrier function is reduced by (at least) some constant factor (smaller than one). In his paper Iri adopts the 'kernel{index tensor notation with Einstein's summation convention for the coordinate indices'. This notation is quite di erent from what is usual in the eld and probably makes the paper unnecessarily di cult to read for those people who are not so familiar with these notational conventions. That is why we decided to rewrite Iri's paper in the standard notation. This is done in the rst six sections of the present working paper. In the last section we specialize to the case that the feasible region is a cone, and we show that the Iri{Imai method, when applying a line search, yields the optimal solution in one step.