A Robust Interior Point Method for Computing the Analytic Center of an Ill-Conditioned Polytope with Errors
Year: 2019
Author: Zhouhong Wang, Yuhong Dai, Fengmin Xu
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 6 : pp. 843–865
Abstract
In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set $P = \{x \in R^n \mid Ax = b, x \ge 0\}$, where the matrix $A \in R^{m\times n}$ is ill-conditioned, and there are errors in $A$ and $b$. Besides overcoming the difficulties caused by ill-conditioning of the matrix $A$ and errors in $A$ and $b$, our method can also detect the infeasibility and the unboundedness of the polyhedral set $P$ automatically during the computation. Detailed mathematical analyses for our method are presented and the worst case complexity of the algorithm is also given. Finally some numerical results are presented to show the robustness and effectiveness of the new method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1907-m2019-0016
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 6 : pp. 843–865
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Analytic center Ill-conditioning Unboundedness Primal-dual interior point algorithm Convergence Polynomial complexity.
Author Details
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