## On two homogeneous self-dual systems for linear programming and its extensions

### Shinji Mizuno and Michael J. Todd

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.

Contact: mizuno@ism.ac.jp, miketodd@cs.cornell.edu