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Conference Papers Year : 2015

Long and Winding Central Paths


We disprove a continuous analog of the Hirsch conjecture proposed by Deza, Terlaky and Zinchenko, by constructing a family of linear programs with 3r+4 inequalities in dimension 2r+2 where the central path has a total curvature in Ω(2^r/r). Our method is to tropicalize the central path in linear programming. The tropical central path is the piecewise-linear limit of the central paths of parameterized families of linear programs viewed through logarithmic glasses.
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hal-01263337 , version 1 (27-01-2016)


  • HAL Id : hal-01263337 , version 1


Xavier Allamigeon, Pascal Benchimol, Stephane Gaubert, Michael Joswig. Long and Winding Central Paths. SIAM Conference on Control and its Applications (SIAM CT’15), Jul 2015, Paris, France. ⟨hal-01263337⟩
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