A Polynomial-Time Affine-Scaling Method for Semidefinite and Hyperbolic   Programming
  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. 
James Renegar and Mutiara Sondjaja
math.OC