An infeasible primal–dual interior point algorithm for linear programs based on logarithmic equivalent transformation

In this paper, we analyze the effect of making algebraically equivalent transformations for the standard centering equation Xs=μe, and specifically consider two cases: power transformation and logarithmic transformation. Especially, for the last case, an infeasible long-step primal–dual path following interior point algorithm is developed, and its global convergence analysis and polynomial-time complexity bound are also given.