Newton Flow and interior Point Methods in Linear Programming

@article{Dedieu2005NewtonFA,
  title={Newton Flow and interior Point Methods in Linear Programming},
  author={Jean-Pierre Dedieu and Michael Shub},
  journal={I. J. Bifurcation and Chaos},
  year={2005},
  volume={15},
  pages={827-839}
}
In this paper we take up once again the subject of the geometry of the central paths of linear programming theory. We study the boundary behavior of these paths as in Meggido and Shub [5], but from a different perspective and with a different emphasis. Our main goal will be to give a global picture of the central paths even for degenerate problems as solution curves of the Newton vector field, N(x), of the logarithmic barrier function which we describe below. See also Bayer and Lagarias [1], [2… CONTINUE READING

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