Long-step primal-dual target-following algorithms for linear programming

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract In this paper we propose a method for linear programming with the property that, starting from an initial non{central point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow so{called targets, that are updated with long steps. Newton's method is used to nd an iterate close to a target. Along with the convergence analysis we provide a general framework which 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.