An interior point method, based on rank-1 updates, for linear programming

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual iterates xk and sk are not needed explicitly in the algorithm whereas d and v are iterated so that the interior primal dual solutions can always be recovered by afore mentioned relations between xk sk and dk vk with improving primal dual potential function values Moreover no approximation of d is needed in the computation of projection directions