## Advances in mathematical optimization: invited papers dedicated to Prof. Dr. Dr. h.c. F. Nožička on occasion of his 70th birthday |

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### Contents

This paper Is intended to complete a stability theory of quasiconvex | 21 |

As usual we understand by a quasiconvex function f on a convex set | 32 |

2 HumboldtUnlversltfit zu Berlin Sektlon Mathematik PSF 1297 | 63 |

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algorithm arbitrary assume assumption Banach space Berlin closed Compute consider constraints continuous convergence convex functions convex sets Corollary corresponding defined denote differentiable doubly stochastic equation equivalent exists finite folgt fulfilled function f gilt given Guddat Hence holds Humboldt-Universitat implies index set inequality infimum Jongen Kuhn-Tucker Lagrange multipliers lattice Lemma LICQ line search linear subspace linearly independent looal mapping Math Mathematical Mathematik matrix method mexqoad multifunction multipliers necessary conditions nonempty nonlinear programming obtain obviously optimal input optimal solution optimization problems parametric optimization point of Type problem 2.3 problem P(t Proof Proposition quadratic quadratic programming quasi-differentiable quasiconvex polynomial recession cone region of stability respectively s.index(y satisfies Satz Section sequence set covering problem slabs solvable solve stationary point stationary solution stochastic programming structural optima subgradient subset Theorem tion upper bound vector VuEB