## Mathematical Programming Study, Volumes 7-9 |

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### Contents

2 Some pivot schemes for the linear complementarity problem C | 15 |

3 An efficient implementation of the Lemke algorithm and its extension | 36 |

4 Robust implementation of Lemkes method for the linear comple | 55 |

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### Common terms and phrases

adjacent Algorithm Schema applied assume basic vector blocker blocking pair bound cluster colouring column combinatorial complementary cone components computational CONE(D consider constraints convex convex set Corollary corresponding Cottle defined denote dual edges elements equations example exists feasible formulation given graph greedy heuristic Hamiltonian circuit Hence heuristic homotopy hypergraph implies inequality initial integer integer programming iterations Journal L.R. Ford layout Lemke Lemma linear complementarity problem linear program logconcave Mathematical Programming matrix matroids maximal minimal nodes nonlinear nonlinear programming nonnegative objective function obtained Operations Research optimal solution optimum orthogonal P-matrix paper partial ordering partition path perfect matching permutation polyhedra polyhedron positive primal algorithm proof satisfying Section sequence simplex method solving Step stochastic programming structure subset Suppose terminates Theorem theory triangulations variables vector vertex vertices zero