Abstract
We applied the modified barrier function (MBF) method and its new extensions to the linear programming (LP) problem and compared with the known LP barrier method. We then extended to the MBF LP method the worst case estimate O( L√ m) for the computational cost of the solution of an LP problem (having input size L and the number of constraints and variables m) in terms of the number of Newton's steps (such an estimate is well-known for the LP barrier methods), and we showed the improved numerical stability of Newton's steps compared with the LP barrier methods.
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