On two homogeneous self-dual approaches to linear programming and its extensions

We investigate the relation between interior-point algorithms applied to two homogeneous self-dual approaches to linear programming, one of which was proposed by Ye, Todd, and Mizuno and the other by Nesterov, Todd, and Ye. We obtain only a partial equivalence of path-following methods (the centering parameter for the first approach needs to be equal to zero or larger than one half), whereas complete equivalence of potential-reduction methods can be shown. The results extend to self-scaled conic programming and to semidefinite programming using the usual search directions.