Buch, Englisch, 272 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 533 g
Buch, Englisch, 272 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 533 g
ISBN: 978-0-521-79133-5
Verlag: Cambridge University Press
Polyhedral functions provide a model for an important class of problems that includes both linear programming and applications in data analysis. General methods for minimizing such functions using the polyhedral geometry explicitly are developed. Such methods approach a minimum by moving from extreme point to extreme point along descending edges and are described generically as simplicial. The best-known member of this class is the simplex method of linear programming, but simplicial methods have found important applications in discrete approximation and statistics. The general approach considered in this 2001 text has permitted the development of finite algorithms for the rank regression problem. The key ideas are those of developing a general format for specifying the polyhedral function and the application of this to derive multiplier conditions to characterize optimality. Also considered is the application of the general approach to the development of active set algorithms for polyhedral function constrained problems and associated Lagrangian forms.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
- Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
Weitere Infos & Material
1. Some basic convex analysis; 2. Introduction to Polyhedra functions; 3. Linear programming algorithms; 4. Piecewise linear separable problems; 5. Rank regression problems; 6. Polyhedral constrained optimization.
