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International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 209-224
http://dx.doi.org/10.1155/S0161171293000262

A center of a polytope: An expository review and a parallel implementation

Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA

Received 1 March 1992

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The solution space of the rectangular linear system Ax=b, subject to x0, is called a polytope. An attempt is made to provide a deeper geometric insight, with numerical examples, into the condensed paper by Lord, et al. [1], that presents an algorithm to compute a center of a polytope. The algorithm is readily adopted for either sequential or parallel computer implementation. The computed center provides an initial feasible solution (interior point) of a linear programming problem.