Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems

@article{Todd1986PolynomialEB,
  title={Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems},
  author={Michael J. Todd},
  journal={Mathematical Programming},
  year={1986},
  volume={35},
  pages={173-192}
}
We show that a particular pivoting algorithm, which we call the lexicographic Lemke algorithm, takes an expected number of steps that is bounded by a quadratic inn, when applied to a random linear complementarity problem of dimensionn. We present two probabilistic models, both requiring some nondegeneracy and sign-invariance properties. The second distribution is concerned with linear complementarity problems that arise from linear programming. In this case we give bounds that are quadratic in… CONTINUE READING

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