A Robust Interior Point Method for Computing the Analytic Center of an Ill-Conditioned Polytope with Errors

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

Zhouhong Wang

Yuhong Dai

Fengmin Xu

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