The Nonlinear Geometry of Linear Programming. III Projective Legendre Transform Coordinates and Hilbert Geometry

J. C. Lagarias
1990 Transactions of the American Mathematical Society  
This paper studies projective scaling trajectories, which are the trajectories obtained by following the infinitesimal version of Karmarkar's linear programming algorithm. A nonlinear change of variables, projective Legendre transform coordinates, is introduced to study these trajectories. The projective Legendre transform mapping has a coordinate-free geometric interpretation in
doi:10.2307/2001758 fatcat:6v6edxrd6rdofi7x5mf53eqyam