Path-Following Methods for Linear Programming

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Abstract. In this paper a unified treatment of algorithms is described for linear programming methods based on the central path. This path is a curve along which the cost decreases, and that stays always far from the boundary of the feasible set. Several parameterizations of this curve are described in primal and primal-dual problems, and it is shown how different algorithms are obtained by following the curve using different parameterizations. Polynomial algorithms are obtained by following the curve approximately, and this concept becomes precise by using explicit rules for measuring the proximity of a point in relation to the central path.