A full-Newton step feasible interior-point method for linear optimization based on an equivalent form of the central path

In this work, we present a primal-dual interior-point method for linear optimization based on a new search direction. We consider an equivalent form of the central path and use Newton’s method to get a new search direction. The algorithm uses only full steps which means that no line searches are needed. We show that the iterates are in the neighborhood of the quadratic convergence of the proximity measure of theiterates. Moreover, we derive the iteration- complexity bound which coincides with the best-known iteration bound for small-update methods

Keywords:

Linear optimization , full-Newton step , interior-point method , small- update methods