Rigorous Global Search: Continuous Problems

1996
ISBN: 978-0-7923-4238-0
Verlag: Springer US

Buch, Englisch, Band 13, 264 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1270 g

Reihe: Nonconvex Optimization and Its Applications

This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.

Zielgruppe

Research

Autoren/Hrsg.

Kearfott, R. Baker

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik EDV | Informatik Betriebssysteme Windows Betriebssysteme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Software Engineering Objektorientierte Softwareentwicklung

Inhaltsverzeichnis

1 Preliminaries.- 2 Software Environments.- 3 On Preconditioning.- 4 Verified Solution of Nonlinear Systems.- 5 Optimization.- 6 Non-Differentiable Problems.- 7 Use of Intermediate Quantities in THE Expression Values.- References.