## On Two Homogeneous Self-Dual Systems for Linear Programming and Its Extensions (1998)

Citations: | 1 - 1 self |

### BibTeX

@MISC{Mizuno98ontwo,

author = {Shinji Mizuno and Michael J. Todd},

title = {On Two Homogeneous Self-Dual Systems for Linear Programming and Its Extensions},

year = {1998}

}

### OpenURL

### Abstract

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. Abbreviated title: On two homogeneous systems for LP 1 Introduction Ye, Todd, and Mizuno [23] presented a homogeneous and self-dual interior-point algorithm for solving linear programming (LP) problems. The algorithm can start from arbitrary (infeasible) interior points and achieves the best known complexity in term of the number of iterations without using a big initial constant. Recently, Nesterov, Todd, and Ye [...