## Integer and nonlinear programmingA NATO Summer School held in Bandol, France, sponsored by the Scientific Affairs Division of NATO. |

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### Contents

necessary are ready to transform what has been mainly research into routine | 2 |

the state of the art and at the same time contain new materials and research | 77 |

to all Contributors for their excellent lectures and their friendly cooperation | 87 |

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### Common terms and phrases

Abadie algorithm applied approximation assume basic variables basis branch and bound calculated coefficients column components computational concave consider constraint set convergence convex convex function corresponding cutting plane Dantzig Davidon defined denote determined dual eigenvalues equations evaluations example face feasible solution Fletcher formula given Gomory gradient method Hence hyperplanes inequality integer polyhedron integer programming integer solution inverse matrix iteration Kuhn-Tucker least squares Lemma linear constraints linear least squares linear programming problem lower bound Math mathematical programming matrix maximization minimization minimum multipliers node non-negative nonlinear constraints nonlinear programming number of steps objective function obtained optimal solution optimum orthogonal parameters penalty function pivot positive definite possible procedure quadratic function quadratic programming satisfying second derivative Section sequence simplex method solving special ordered sets subset tableau Theorem unconstrained upper bound vertex Wolfe zero Zoutendijk