Nonlinear Integer Programming

2006
ISBN: 978-0-387-29503-9
Verlag: Springer US

Buch, Englisch, Band 84, 438 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1820 g

Reihe: International Series in Operations Research & Management Science

It is not an exaggeration that much of what people devote in their hfe re­ solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. Since the pioneering work of R. Gomory [80] in the late 1950s, the theoretical and methodological development of integer programming has grown by leaps and bounds, mainly focusing on linear integer programming. The past few years have also witnessed certain promising theoretical and methodological achieve­ ments in nonlinear integer programming. When the first author of this book was working on duality theory for n- convex continuous optimization in the middle of 1990s, Prof. Douglas J. White suggested that he explore an extension of his research results to integer pro­ gramming. The two authors of the book started their collaborative work on integer programming and global optimization in 1997. The more they have investigated in nonlinear integer programming, the more they need to further delve into the subject. Both authors have been greatly enjoying working in this exciting and challenging field.

Zielgruppe

Research

Autoren/Hrsg.

Sun, Xiaoling

Li, Duan

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik EDV | Informatik Informatik

Inhaltsverzeichnis

Optimality, Relaxation and General Solution Procedures.- Lagrangian Duality Theory.- Surrogate Duality Theory.- Nonlinear Lagrangian and Strong Duality.- Nonlinear Knapsack Problems.- Separable Integer Programming.- Nonlinear Integer Programming with a Quadratic Objective Function.- Nonseparable Integer Programming.- Unconstrained Polynomial 0–1 Optimization.- Constrained Polynomial 0–1 Programming.- Two Level Methods for Constrained Polynomial 0–1 Programming.- Mixed-Integer Nonlinear Programming.- Global Descent Methods.