# 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} }

- Published in Math. Program. 1986
DOI:10.1007/BF01580646

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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