A Path-Following Projective Interior Point Method for Linear Programming

@article{Shaw1994APP,
  title={A Path-Following Projective Interior Point Method for Linear Programming},
  author={Dong X. Shaw and Donald Goldfarb},
  journal={SIAM Journal on Optimization},
  year={1994},
  volume={4},
  pages={65-85}
}
In this paper the authors present a projective interior point method which follows the "central trajectory" and finds an optimal solution in at most O(vL) iterations. This algorithm is essentially Anstreicher’s variant of Karmarkar’s projective algorithm with a weakened "ball update" for lower bounds. The result indicates that a strong relationship exists between projective and pathfollowing algorithms. The authors show that within a certain probabilistic framework the expected number of… CONTINUE READING

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