Interior path following primal-dual algorithms. part I: Linear programming

@article{Monteiro1989InteriorPF,
  title={Interior path following primal-dual algorithms. part I: Linear programming},
  author={R. C. Monteiro and I. Adler},
  journal={Mathematical Programming},
  year={1989},
  volume={44},
  pages={27-41}
}
AbstractWe describe a primal-dual interior point algorithm for linear programming problems which requires a total of $$O\left( {\sqrt n L} \right)$$ number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea. 
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