A SURFACE OF ANALYTIC CENTERS AND PRIMAL-DUAL INFEASIBLE-INTERIOR-POINT ALGORITHMS FOR LINEAR-PROGRAMMING

We define a surface of analytic centers determined by a primal-dual pair of linear programming problems and an infeasible interior point. Then we study the boundary; of the surface by analyzing limiting behavior of paths on the surface and sequences in a neighborhood of the surface. We introduce generic primal-dual infeasible-interior-point algorithms in which the search direction is the Newton direction for a system defining a paint on the surface. We show that feasible-interior-point algorithms for artificial self-dual problems and for an artificial primal-dual pair of linear programming problems can be considered as special cases of these infeasible-interior-point algorithms or simple variants of them. In this sense, there are O(root nL)-iteration primal-dual infeasible-interior-point algorithms for linear programming.