  We disprove a continuous analogue 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 $\Omega(2^r)$. 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 classical linear programs viewed
through logarithmic glasses. The lower bound for the classical curvature is
obtained by developing a combinatorial concept of a tropical angle.

Optimization and Control;Combinatorics