  We develop a natural variant of Dikin's affine-scaling method, first for
semidefinite programming and then for hyperbolic programming in general. We
match the best complexity bounds known for interior-point methods.
  All previous polynomial-time affine-scaling algorithms have been for conic
optimization problems in which the underlying cone is symmetric. Hyperbolicity
cones, however, need not be symmetric. Our algorithm is the first
polynomial-time affine-scaling method not relying on symmetry.
