Overview
- A combination of both Integer Programming and Nonlinear Optimization. Therefore, it will be a powerful book that surveys the field and provides a state-of-the-art treatment of Nonlinear Integer Programming
- The first book available on the area. As the reviewers note, the authors have achieved considerable advances in recent years and the book will summarize the field and its most recent results
- The authors' English is excellent. The book is written at the level of graduate students and it will be accessible to a wide audience of researchers, students, and practitioners
- Includes supplementary material: sn.pub/extras
Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 84)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
"This book addresses the topic of the general nonlinear integer programming (NLIP). The overall goal of the book is to bring the state of the art of the theoretical foundations and solution methods of NLIP to readers who are interested in optimization, operations research and computer science. This book investigates the theory and solution methodologies for the general NLIP and provides the developments of the last 30 years. It is assumed that readers are familiar with linear integer programming and the book thus focuses on the theory and solution methodologies of NLIP. The following are some of the features of the book: \roster \item"$\bullet$" Duality theory for NLIP: Investigation into the relationship of the duality gap and the perturbation function has lead to the development of nonlinear Lagrangian theory, thus establishing a methodology for the solution of the NLIP. \item"$\bullet$" Convergent Lagrangian and cutting plane methods for NLIP: Concepts like the objective level cuts, objective contour cuts or the domain cut reshapes the perturbation function. This leads to the optimal solution to lie in the convex hull of the perturbation functions and thus guarantees a zero duality gap. \item"$\bullet$" Convexification scheme: Using the connection between monotonicity and convexity, convexification schemes are developed for monotone and non-convex integer programs, thus extending the reach of branch and bound methods. \item"$\bullet$" Solution framework using global descent: The optimal solution of an NLIP is sought from among the local minima. A theoretical framework is also established to escape from a local minimum. \item"$\bullet$" Computational implications for NLIP: Several NLIPs with up to several thousand variables are solved by solution algorithms presented in this book." (Romesh Saigal, Mathematical Reviews)
"The book’s goal is to bring the state-of-the-art NIP theoretical foundation and solutionmethods to students and researchers in optimization, OR, and computer science. … I think this is an interesting book about NIP and related issues. Many students, professionals, professors, and researchers could use it to learn key concepts about this topic. Therefore, I consider this work a valuable reference for graduate students or researchers interested in integer programming in a wide sense … ." (Javier Faulin, Interfaces, Vol. 37 (4), 2007)
"The goal of the book is to bring the state-of-the-art of the theoretical foundation and solution methods for nonlinear integer programming to readers who are interested in optimization, operations research and computer science. … Readers of this book can be researchers, practitioners, graduate students and senior undergraduate students … . It can be also used as a reference book for researchers, engineers and practitioners to solve real-world application problems by nonlinear integer programming models." (Oleg A. Shcherbina, Zentralblatt MATH, Vol. 1140, 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Nonlinear Integer Programming
Authors: Duan Li, Xiaoling Sun
Series Title: International Series in Operations Research & Management Science
DOI: https://doi.org/10.1007/0-387-32995-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2006
Hardcover ISBN: 978-0-387-29503-9Published: 03 May 2006
Softcover ISBN: 978-1-4419-3991-3Published: 19 November 2010
eBook ISBN: 978-0-387-32995-6Published: 13 August 2006
Series ISSN: 0884-8289
Series E-ISSN: 2214-7934
Edition Number: 1
Number of Pages: XXII, 438
Topics: Optimization, Operations Research/Decision Theory, Operations Research, Management Science, Mathematical Modeling and Industrial Mathematics, Mathematics of Computing, Math Applications in Computer Science