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Warm-start strategies in interior-point
methods for linear programming

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E. Alper Yildirim and Stephen J. Wright

We study the situation in which, having solved a linear program with
an interior-point 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.
Technical Report 1258, School of Operations Research and
Industrial Engineering, Cornell University

Preprint MCS-P799-0300, Mathematics and Computer Science Division,
Argonne National Laboratory.

Contact: yildirim@orie.cornell.edu, wright@mcs.anl.gov