Maintaining closeness to the analytic center of a polytope by perturbing added hyperplanes

Maintaining closeness to the analytic center of a polytope by perturbing added hyperplanes In this work we consider a region R in ℝ n given by a finite number of linear inequalities and having nonempty interior. We assume a point x o is given, which is close in certain norm to the analytic center of R , and that a new linear inequality is added to those defining R . It is constructively shown how to obtain a perturbation of the right-hand side of this inequality such that the point x 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Maintaining closeness to the analytic center of a polytope by perturbing added hyperplanes

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683324
Publisher site
See Article on Publisher Site

Abstract

In this work we consider a region R in ℝ n given by a finite number of linear inequalities and having nonempty interior. We assume a point x o is given, which is close in certain norm to the analytic center of R , and that a new linear inequality is added to those defining R . It is constructively shown how to obtain a perturbation of the right-hand side of this inequality such that the point x 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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 1, 1997

References

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