Abstract
In this work we consider a regionR in ℝ n given by a finite number of linear inequalities and having nonempty interior. We assume a pointx o is given, which is close in certain norm to the analytic center ofR, and that a new linear inequality is added to those definingR. It is constructively shown how to obtain a perturbation of the right-hand side of this inequality such that the pointx o is still close, in the same norm, to the analytic center of this perturbed polytope. This fact plays a central role in interior point postoptimality techniques for linear programming involving methods of centers.
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