Algorithms for Continuous Optimization

1. Front Matter

   Pages i-xv

   PDF

2. General Optimality Conditions via a Separation Scheme

   • Franco Giannessi

   Pages 1-23

3. Linear Equations in Optimisation

   • C. G. Broyden

   Pages 25-35

4. Generalized and Sparse Least Squares Problems

   • Åke Björck

   Pages 37-80

5. Algorithms for Solving Nonlinear Systems of Equations

   • José Mario Martínez

   Pages 81-108

6. An Overview of Unconstrained Optimization

   • R. Fletcher

   Pages 109-143

7. Nonquadratic Model Methods in Unconstrained Optimization

   • N. Y. Deng, Z. F. Li

   Pages 145-168

8. Algorithms for General Constrained Nonlinear Optimization

   • M. C. Bartholomew-Biggs

   Pages 169-207

9. Exact Penalty Methods

   • G. Di Pillo

   Pages 209-253

10. Stable Barrier-Projection and Barrier-Newton Methods for Linear and Nonlinear Programming

    • Yu. G. Evtushenko, V. G. Zhadan

    Pages 255-285

11. Large-scale Nonlinear Constrained Optimization: a Current Survey

    • Andrew R. Conn, Nick Gould, Philippe L. Toint

    Pages 287-332

12. ABS Methods for Nonlinear Optimization

    • Emilio Spedicato, Zunquan Xia

    Pages 333-356

13. A Condensed Introduction to Bundle Methods in Nonsmooth Optimization

    • C. Lemaréchal, J. Zowe

    Pages 357-382

14. Computational Methods For Linear Programming

    • D. F. Shanno

    Pages 383-413

15. Infeasible Interior Point Methods for Solving Linear Programs

    • J. Stoer

    Pages 415-434

16. Algorithms for Linear Complementarity Problems

    • Joaquim J. Júdice

    Pages 435-474

17. A Homework Exercise — The “Big-M” Problem

    • R. W. H. Sargent

    Pages 475-479

18. Deterministic Global Optimization

    • Yu. G. Evtushenko, M. A. Potapov

    Pages 481-500

19. On Automatic Differentiation and Continuous Optimization

    • L. C. W. Dixon

    Pages 501-512

20. Neural Networks and Unconstrained Optimization

    • L. C. W. Dixon

    Pages 513-530

The NATO Advanced Study Institute on "Algorithms for continuous optimiza­ tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza­ tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel­ oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob­ jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.

• algorithms
• differential equation
• linear optimization
• network
• networks
• neural networks
• nonlinear optimization
• optimization
• programming

• Department of Mathematics, University of Bergamo, Bergamo, Italy

  Emilio Spedicato

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