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- W2081321954 abstract "Abstract The problem of finding a deepest point (a ball centre) of a polyhedron is studied. A finite combinatorial interior point method is presented for this problem which yields an algorithm for linear programming. We conjecture that this is a strongly polynomial algorithm. Meanwhile developing the algorithm, several auxiliary results were found; among others, Gorokh and Werner’s algorithm for linear inequalities is slightly extended. Our numerical experiments with the problem detected bugs in a linear interior point solver used in MATLAB 6 Optimization Toolbox. Keywords: linear inequalitiesdeepest point of polyhedronball centrelinear programminginterior point methodbad examplesAMS Subject Classifications: 90C0590C0890C4690C51 Acknowledgments We would like to thank the referee for his/her valuable comments and suggestions that improved the paper. The research was supported by the Slovak Scientific Grant Agency VEGA (Nos. 1/0406/09 and 1/1005/12)." @default.
- W2081321954 created "2016-06-24" @default.
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- W2081321954 date "2013-01-30" @default.
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- W2081321954 title "Deepest point of a polyhedron and linear programming" @default.
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- W2081321954 doi "https://doi.org/10.1080/02331934.2012.756877" @default.
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