Warm-Start Strategies in Interior-Point Methods for Linear Programming

We study the situation in which, having solved a linear program with an interiorpoint method, we are presented with a new problem instance whose data is slightly perturbed from the original. We describe strategies for recovering a \warm-start" point for the perturbed problem instance from the iterates of the original problem instance. We obtain worst-case estimates of the number of iterations required to converge to a solution of the perturbed instance from the warm-start points, showing that these estimates depend on the size of the perturbation and on the conditioning and other properties of the problem instances.