Abstract : 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.
https://hal.inria.fr/hal-01263337
Contributor : Marianne Akian <>
Submitted on : Wednesday, January 27, 2016 - 4:31:37 PM Last modification on : Friday, April 30, 2021 - 9:57:58 AM
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⟩