A simplified homogeneous and self-dual linear programming algorithm and its implementation

Abstract

We present a simplification and generalization of the recent homogeneous and self-dual linear programming (LP) algorithm. The algorithm does not use any Big-M initial point and achieves$O(\sqrt {nL} )$-iteration complexity, wheren andL are the number of variables and the length of data of the LP problem. It also detects LP infeasibility based on a provable criterion. Its preliminary implementation with a simple predictor and corrector technique results in an efficient computer code in practice. In contrast to other interior-point methods, our code solves NETLIB problems, feasible or infeasible, starting simply fromx=e (primal variables),y=0 (dual variables),z=e (dual slack variables), wheree is the vector of all ones. We describe our computational experience in solving these problems, and compare our results with OB1.60, a state-of-the-art implementation of interior-point algorithms.