An iteration bound primal-dual cone affine scaling algorithm for linear programming

In this paper the authors introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions, nor does it fit in the general primal-dual method. The new method requires main iterations. It is shown that the iterates follow the primal-dual central path in a neighbourhood large than the conventional neighbourhood. The proximity to the primal-dual central path is measured by trigonometric functions.