Algorithms for Continuous Optimization

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.

Klappentext

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.

Inhalt

1. General Optimality Conditions via a Separation Scheme.- 2. Linear Equations in Optimisation.- 3. Generalized and Sparse Least Squares Problems.- 4. Algorithms for Solving Nonlinear Systems of Equations.- 5. An Overview of Unconstrained Optimization.- 6. Nonquadratic Model Methods in Unconstrained Optimization.- 7. Algorithms for General Constrained Nonlinear Optimization.- 8. Exact Penalty Methods.- 9. Stable Barrier-Projection and Barrier-Newton Methods for Linear and Nonlinear Programming.- 10. Large-scale Nonlinear Constrained Optimization: a Current Survey.- 11. ABS Methods for Nonlinear Optimization.- 12. A Condensed Introduction to Bundle Methods in Nonsmooth Optimization.- 13. Computational Methods for Linear Programming.- 14. Infeasible Interior Point Methods for Solving Linear Programs.- 15. Algorithms for Linear Complementarity Problems.- 16. A Homework Exercise the Big M Problem.- 17. Deterministic Global Optimization.- 18. On Automatic Differentiation and Continuous Optimization.- 19. Neural Networks and Unconstrained Optimization.- 20. Parallel Nonlinear Optimization: Limitations, Challenges and Opportunities.