## Nonlinear Optimization and Related TopicsThis volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume. |

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### Contents

15 | |

Minimal convexificators of a positively homogeneous function and a characterization | 50 |

Optimal control problems and penalization | 67 |

Fixed and virtual stability center methods for convex nonsmooth minimization 105 | 104 |

Iterative methods for illconditioned linear systems from optimization | 123 |

An algorithm for solving nonlinear programs with noisy inequality constraints | 143 |

Generic existence uniqueness and stability in optimization problems 169 | 168 |

Alexander Ioffe Roberto Lucchetti | 183 |

Separation methods for vector variational inequalities Saddle point and | 207 |

Quadratic and multidimensional assignment problems 235 | 234 |

A new merit function and an SQP method for nonstrictly monotone variational | 257 |

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algorithm analysis applications approach approximation assignment assume assumptions bounded complementarity computational consider constant constraints continuous convergence convex corresponding defined definite denote derivative descent differentiable direction dual element equality equation equivalent exact example exists feasible formulation give given global gradient Hence holds implies introduced iteration Journal Lagrange Lagrangian Lemma linear Lipschitz lower Mathematical Programming matrix merit function method minimization monotone Moreover multiplier nonlinear programming nonsmooth Note objective observe obtain operator optimization problem parameter penalty positive possible present problem programming Proof properties proposed Proposition prove quadratic Related Remark respect rule satisfies sequence SIAM smooth solution solving space Step strongly structure sufficient Suppose Table Theorem Theory variables variational inequality vector yields zero