A new infeasible interior-point algorithm for linear programming

Abstract

In this paper we present an infeasible path-following interior-point algorithm for solving linear programs using a relaxed notion of the central path, called quasicentral path, as a central region. The algorithm starts from an infeasible point which satisfies that the norm of the dual condition is less than the norm of the primal condition. We use weighted sets as proximity measures of the quasicentral path, and a new merit function for making progress toward this central region. We test the algorithm on a set of NETLIB problems obtaining promising numerical results.