A Weighted-path-following Method for Linear Optimization

In a recent paper [4] we introduced a new method for finding search directions for interior point methods (IPMs) in linear optimization (LO), and we developed a new polynomial algorithm for solving LO problems. It is well-known that using the self-dual embedding we can find a starting feasible solution, and this point will be on the central path. We proved [3] that this initialization method can be applied for the new algorithm as well. However, practical implementations often don’t use perfectly centered starting points. Therefore it is worth analysing the case when the starting point is not on the central path. In this paper we develop a new weighted-path-following algorithm for solving LO problems. We conclude that following the central path yields to the best iteration bound in this case as well.