## Nonlinear Programming |

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### Contents

Optimality Criteria in Nonlinear Programming | 27 |

Some Global Convergence Properties of a Variable Metric Algorithm | 53 |

A Short Course in Solving Equations with PL Homotopies | 73 |

Copyright | |

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### Common terms and phrases

0f course 0perations Research 0ptimization 1-manifold Academic Press algorithm Applications approximation augmented Lagrangian BFGS bounded Broyden Broyden's method calculation Calculus of Variations cell Complementary Pivot computational constraint qualification convex analysis convex function convex set defined Dennis Department of 0perations duality eigenvalues equations equivalent Example exist F(xJ feasible solutions Fixed Points function f given global gradient hence Hessian Hestenes inequality iteration Karush Kuhn and Tucker Lagrange multiplier Lagrangian Lemke Lemma line search Linear Complementarity Problem linear program m-cell Mangasarian manifold Math Mathematical Programming matrix minimization minimum necessary conditions Nonlinear Complementarity Problem Nonlinear Programming optimization problems orientation paper penalty PL map positive definite Powell programming problem Proof properties quasi-Newton methods rate of convergence regular point regular value result route saddle point satisfied second derivatives Section sequence SIAM simplex Stanford steepest descent subdivided sufficient conditions superlinear Theorem tion triangulation unconstrained University variable metric Vf(x