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# Nonlinear Integer Programming by Duan Li

Condition - New
$277.79 Only 2 left ## Summary A combination of both Integer Programming and Nonlinear Optimization, this is a powerful book that surveys the field and provides a state-of-the-art treatment of Nonlinear Integer Programming. This book will be specially printed for your order, which means it may take a little longer to arrive (5 days). We do this to cut down on waste & to help protect our planet. ## Nonlinear Integer Programming Summary ### Nonlinear Integer Programming by Duan Li A combination of both Integer Programming and Nonlinear Optimization, this is a powerful book that surveys the field and provides a state-of-the-art treatment of Nonlinear Integer Programming. It is the first book available on the subject. The book aims to bring the theoretical foundation and solution methods for nonlinear integer programming to students and researchers in optimization, operations research, and computer science. ## Nonlinear Integer Programming Reviews From the reviews: "This book addresses the topic of the general nonlinear integer programming (NLIP). The overall goal of the book is to bring the state of the art of the theoretical foundations and solution methods of NLIP to readers who are interested in optimization, operations research and computer science. This book investigates the theory and solution methodologies for the general NLIP and provides the developments of the last 30 years. It is assumed that readers are familiar with linear integer programming and the book thus focuses on the theory and solution methodologies of NLIP. The following are some of the features of the book: \roster \item"$\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 solution methods 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)

## Table of Contents

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.

## Additional information

NLS9781441939913
9781441939913
1441939911
Nonlinear Integer Programming by Duan Li
New
Paperback
Springer-Verlag New York Inc.
2010-11-19
438
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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