## A generalized derivative and its applications to optimization theory, classical analysis, and global univalence |

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### Contents

THE LIPSCHITZ INTERIOR MAPPING | 20 |

PART in APPLICATIONS | 30 |

THE GENERAL LIPSCHITZ MULTIPLIER | 38 |

2 other sections not shown

### Common terms and phrases

affine path assume assumption boundedness Brouwer degree choose classical compact subset continuation property contradicting convex hull convex set convex subset Corollary 17 cp(a cp(z define deg(f derivative 3f(a domain f equality constraints exists f is Lipschitz f is univalent follows Gale and Nikaido global univalence Hadamard Hadamard matrices hence homeomorphism implies inequality infer int f(U interior mapping theorem Inverse Mapping Theorem IRn into IRn L(IR L(IRn Lebesgue point Lebesgue set Lemma let f lim a(t linear maps Lipschitz continuous functions Lipschitz continuous mapping Lipschitz Multiplier Rule matrix Mean Value Theorem natural number neighborhood open set open subset Optimization Theory P-matrix positive definite principal submatrix Proof of Theorem Proposition 19 prove result sequence sign det 3f(x strong derivative strongly differentiable subset of IRn Suppose f Suppose that f surjective Theorem 11 Theorem 3.2 theorem for Lipschitz uniform convergence W. H. Young whence