## Karmarkar's algorithm and combinatorial optimization problems |

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### Contents

A Variant of Karmarkars Algorithm for Problems with some Unre | 17 |

An Algorithm for Solving Combinatorial Optimization Problems | 34 |

The Perfect Matching Problem | 76 |

Copyright | |

5 other sections not shown

### Common terms and phrases

adding cutting planes adding edges adding variables affine hull algorithm to solve bucket sort Chapter combinatorial optimization combinatorial optimization problems combinatorial problem complete graph component convex hull corresponding current relaxation cutting planes added defined digraph direction dual linear program equation facets feasible solution Grotschel and Holland hyperplane inequalities interior feasible point interior point interior point method iterations of Karmarkar's Karmarkar's algorithm Karush-Kuhn-Tucker conditions least squares problem Lemma linear ordering problem linear programming problem linear programming relaxation lower bound LP relaxation max bTy max z s.t. null space number of edges number of iterations Number of stages objective function optimal solution optimal value p-vectors perfect matching problem Phase I procedure Pm(G polytope primal solution QR-factorization reduced cost s.t. Ax search strategy separation routines simplex algorithm sixty node problems stages of adding standard choice step length strictly positive feasible unrestricted variables updated variant of Karmarkar's vertex vertices violated constraints