Long-Step Primal-Dual Target-Following Algorithms for Linear Programming

In this paper we propose a long-step target-following methodology for linear programming. This is a general framework, that enables us to analyze various long-step primal-dual algorithms in the literature in a short and uniform way. Among these are long-step central and weighted path-following methods and algorithms to compute a central point or a weighted center. Moreover, we use it to analyze a method with the property that it, starting from an initial non-central point, generates iterates that simultaneously get closer to optimality and closer to centrality