Polytopes and arrangements: Diameter and curvature

@article{Deza2008PolytopesAA,
  title={Polytopes and arrangements: Diameter and curvature},
  author={Antoine Deza and Tam{\'a}s Terlaky and Yuriy Zinchenko},
  journal={Oper. Res. Lett.},
  year={2008},
  volume={36},
  pages={215-222}
}
By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities deflning the polytope. By analogy with a result of Dedieu, Malajovich and Shub, we conjecture that the average diameter of a bounded cell of an arrangement is less than the dimension. We prove continuous analogues of two results of Holt-Klee and Klee-Walkup: we construct a family of polytopes which attain the conjectured… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 19 references

Shub: Newton °ow and interior point pethods in linear programming

  • M.J.-P. Dedieu
  • International Journal of Bifurcation and Chaos
  • 2005
Highly Influential
6 Excerpts

Vial: Interior Point Methods for Linear Optimization

  • C. Roos, T. Terlaky, J.-Ph
  • 2006
3 Excerpts

Newton ° ow and interior point pethods in linear programming

  • T. Terlaky Deza
  • International Journal of Bifurcation and Chaos
  • 2005

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