Finding exact corner solutions to linear programming using interior point methods
You might want to read the paper:


  Sanjay Mehrotra, On finding a vertex solution using interior point methods, Linear Algebra and its Applications, Volume 152, 1 July 1991, Pages 233-253, ISSN 0024-3795, 10.1016/0024-3795(91)90277-4. sciencedirect article link