## Computational practice in mathematical programming |

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### Contents

2 Partially normalized pivot selection in linear programming | 12 |

3 An exact update for Harris TREAD Harvey J Greenberg | 26 |

5 A synthesis of compactinverse methods for blockangular linear | 58 |

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### Common terms and phrases

approximation backward transformation basic in explicit basic in VUB basic variables basis change basis inverse block-angular branch and bound coefficients column selection computed core decomposition dual multiple pricing E.M.L. Beale effective elementary row operations enter the basis experiments explicit row G.B. Dantzig gradient identity matrix ineffective integer programming integer variables inverse matrix iteration counts iteration X linear programming problems mathematical programming systems minimize negative negative cost non-basic variables non-zero elements nonlinear nonlinear programming nonzero number of iterations number of segments number of variables objective function partial norm PFLP pivot column pivot row selection pricing and suboptimization primal procedure product form algorithm quadratic programming reduced costs reduced product form replaced row q scaling simplex algorithm simplex method slack variable solved standard simplex step subproblem subspace tableau techniques TREAD triangular factors updated upper bounds VUB constraints VUB row xj is basic zero