An O(√n L) iteration bound primal-dual cone affine scaling algorithm for linear programming

In this paper we 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 (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method requires O(√n L) main iterations. It is shown that the iterates follow the primal-dual central path in a neighbourhood larger than the conventional script N sign₂ neighbourhood. The proximity to the primal-dual central path is measured by trigonometric functions.