Nonlinear Optimization and Applications

This volume contains the edited texts of the lectures presented at the workshop on Nonlinear Optimization: Theory and Applications, held in Erice at the "G. Stampacchia" School of Mathematics of the "E. Majorana" International Centre for Scientific Culture June 13-21, 1995. The meeting was conceived to review and discuss recent advances and promising research trends concerning theory, algorithms, and innovative applications in the field This is a field of mathematics which is providing viable of Nonlinear Optimization. tools in engineering, in economics and in other applied sciences, and which is giving a great contribution also in the solution of the more practiced linear optimization prob­ lems. The meeting was attended by approximately 70 people from 18 countries. Besides the lectures, several formal and informal discussions took place. The result was a broad exposure providing a wide and deep understanding of the present research achievements in the field. We wish to express our appreciation for the active contributions of all the partici­ pants in the meeting. Our gratitude is due to the Ettore Majorana Center in Erice, which offered its facilities and stimulating environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massino Roma for the time spent in the organization of the workshop, and to Giuliana Cai for the careful typesetting of this volume. Front Matter....Pages i-xii Towards a Discrete Newton Method with Memory for Large-Scale Optimization....Pages 1-12 On Regularity for Generalized Systems and Applications....Pages 13-26 An Algorithm using Quadratic Interpolation for Unconstrained Derivative Free Optimization....Pages 27-47 Massively Parallel Solution of Large Scale Network Flow Problems....Pages 49-59 Correction Theorems for Nonsmooth Systems....Pages 61-74 Successive Projection Methods for the Solution of Overdetermined Nonlinear Systems....Pages 75-84 On Exact Augmented Lagrangian Functions in Nonlinear Programming....Pages 85-100 Space-Transformation Technique: The State of the Art....Pages 101-123 Inexact Newton Methods for Semismooth Equations with Applications to Variational Inequality Problems....Pages 125-139 Accessing Realistic Mixed Complementarity Problems within MATLAB....Pages 141-153 Merit Functions for Variational Inequality and Complementarity Problems....Pages 155-170 Some Remarks on Penalization for Variational Inequalities and Generalizations....Pages 171-179 Globally Convergent Online Minimization Algorithms for Neural Network Training....Pages 181-195 Semismoothness and Superlinear Convergence in Nonsmooth Optimization and Nonsmooth Equations....Pages 197-212 On the Solution of the Monotone and Nonmonotone Linear Complementarity Problem by an Infeasible Interior-Point Algorithm....Pages 213-227 Ergodic Results in Subgradient Optimization....Pages 229-248 Proto-Derivatives and the Geometry of Solution Mappings in Nonlinear Programming....Pages 249-260 Numerical Results for Unconstrained Optimization without Derivatives....Pages 261-270 Hierarchical Systems with Weighted Reaction Set....Pages 271-282 Mathematical Programming in Machine Learning....Pages 283-295 Smoothing Techniques for Macromolecular Global Optimization....Pages 297-312 Continuous Approaches to Discrete Optimization Problems....Pages 313-325 Homotopies Based on Nonsmooth Equations for Solving Nonlinear Variational Inequalities....Pages 327-343 ABS Methods for KT Equations....Pages 345-359 Erratum to: On Exact Augmented Lagrangian Functions in Nonlinear Programming....Pages 369-369 Erratum to: Continuous Approaches to Discrete Optimization Problems....Pages 369-369 Erratum to: Homotopies Based on Nonsmooth Equations for Solving Nonlinear Variational Inequalities....Pages 369-369 Erratum to: ABS Methods for KT Equations....Pages 369-369 Erratum....Pages 369-369 Back Matter....Pages 361-367 This volume contains the edited texts of the lectures presented at the workshop on Nonlinear Optimization: Theory and Applications, held in Erice at the "G. Stampacchia" School of Mathematics of the "E. Majorana" International Centre for Scientific Culture June 13-21, 1995. The meeting was conceived to review and discuss recent advances and promising research trends concerning theory, algorithms, and innovative applications in the field This is a field of mathematics which is providing viable of Nonlinear Optimization. tools in engineering, in economics and in other applied sciences, and which is giving a great contribution also in the solution of the more practiced linear optimization probƯ lems. The meeting was attended by approximately 70 people from 18 countries. Besides the lectures, several formal and informal discussions took place. The result was a broad exposure providing a wide and deep understanding of the present research achievements in the field. We wish to express our appreciation for the active contributions of all the particiƯ pants in the meeting. Our gratitude is due to the Ettore Majorana Center in Erice, which offered its facilities and stimulating environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massino Roma for the time spent in the organization of the workshop, and to Giuliana Cai for the careful typesetting of this volume