Nonlinear Optimization and Related Topics

1. Front Matter

   Pages i-vii

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2. Generalized Lagrange multipliers: regularity and boundedness

   • Giancarlo Bigi, Massimo Pappalardo

   Pages 1-14

3. A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints

   • Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint

   Pages 15-49

4. Minimal Convexificators of a positively Homogeneous Function and a Characterization of Its Convexity and Concavity

   • Vladimir F. Demyanov

   Pages 51-65

5. Optimal Control Problems and Penalization

   • Vladimir F. Demyanov, Franco Giannessi, Vladimir V. Karelin

   Pages 67-78

6. A truncated Newton method for constrained optimization

   • Gianni Di Pillo, Stefano Lucidi, Laura Palagi

   Pages 79-103

7. Fixed and virtual stability center methods for convex nonsmooth minimization

   • Antonio Fuduli, Manlio Gaudioso

   Pages 105-122

8. Iterative methods for ill-conditioned linear systems from optimization

   • Nicholas I. M. Gould

   Pages 123-141

9. An Algorithm for Solving Nonlinear Programs with Noisy Inequality Constraints

   • Michael Hintermüller

   Pages 143-167

10. Generic Existence, Uniqueness and Stability in Optimization Problems

    • Alexander Ioffe, Roberto Lucchetti

    Pages 169-182

11. On a class of bilevel programs

    • Martine Labbé, Patrice Marcotte, Gilles Savard

    Pages 183-206

12. Separation methods for Vector Variational Inequalities. Saddle point and gap function

    • Giandomenico Mastroeni

    Pages 207-217

13. Functions with Primal-Dual Gradient Structure and u-Hessians

    • Robert Mifflin, Claudia Sagastizábal

    Pages 219-233

14. Quadratic and Multidimensional Assignment Problems

    • Panos M. Pardalos, Leonidas S. Pitsoulis

    Pages 235-256

15. A new merit function and an SQP method for non-strictly monotone variational inequalities

    • Michael Patriksson

    Pages 257-275

16. A Logarithmic Barrier Approach to Fischer Function

    • Jiming Peng, Cornelis Roos, Tamás Terlaky

    Pages 277-297

17. On an Approach to Optimization Problems with a Probabilistic Cost and or Constraints

    • Elijah Polak, Roger J.-B. Wets, Armen der Kiureghian

    Pages 299-315

18. Semiderivative Functions and Reformulation Methods for Solving Complementarity and Variational Inequality Problems

    • Liqun Qi, Danny Ralph, Guanglu Zhou

    Pages 317-350

19. Global Lagrange multiplier rule and smooth exact penalty functions for equality constraints

    • Tamás Rapcsák

    Pages 351-368

20. Structural Methods in the Solution of Variational Inequalities

    • Stephen M. Robinson

    Pages 369-380

This 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.

• algorithms
• linear optimization
• nonlinear optimization
• optimal control
• optimization
• programming

• University Di Roma La Sapienza, Italy

  Gianni Di Pillo

• University of Pisa, Italy

  Franco Giannessi

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