Overview

This book addresses a new method for generating tight linear or convex programming relaxations for discrete and continuous nonconvex programming problems. Problems of this type arise in many economics, location-allocation, scheduling and routing, and process control and engineering design applications. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through an automatic reformulation and constraint generation technique. The contents of this book comprise the original work of the authors compiled from several journal publications, and not covered in any other book on this subject. The outstanding feature of this book is that it offers for the first time a unified treatment of discrete and continuous nonconvex programming problems. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. The book lays the foundation of an idea that is stimulating and that has served to enhance the solubility of many challenging problems in the field. Audience: This book is intended for researchers and practitioners who work in the area of discrete or continuous nonlinear, nonconvex optimization problems, as well as for students who are interested in learning about techniques for solving such problems.

Full Product Details

Author:   Hanif D. Sherali ,  W. P. Adams
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1999
Volume:   31
Dimensions:   Width: 15.50cm , Height: 2.70cm , Length: 23.50cm
Weight:   0.825kg
ISBN:  

9781441948083

ISBN 10:   1441948082
Pages:   518
Publication Date:   02 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Introduction.- I Discrete Nonconvex Programs.- 2 RLT Hierarchy for Mixed-Integer Zero-One Problems.- 3 Generalized Hierarchy for Exploiting Special Structures in Mixed-Integer Zero-One Problems.- 4 RLT Hierarchy for General Discrete Mixed-Integer Problems.- 5 Generating Valid Inequalities and Facets Using RLT.- 6 Persistency in Discrete Optimization.- II Continuous Nonconvex Programs.- 7 RLT-Based Global Optimization Algorithms for Nonconvex Polynomial Programming Problems.- 8 Reformulation-Convexification Technique for Quadratic Programs and Some Convex Envelope Characterizations.- 9 Reformulation-Convexification Technique for Polynomial Programs: Design and Implementation.- III Special Applications to Discrete and Continuous Nonconvex Programs.- 10 Applications to Discrete Problems.- 11 Applications to Continuous Problems.- References.

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