A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems

A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems
Author :
Publisher : Springer Science & Business Media
Total Pages : 529
Release :
ISBN-10 : 9781475743883
ISBN-13 : 1475743882
Rating : 4/5 (83 Downloads)

Book Synopsis A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems by : Hanif D. Sherali

Download or read book A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems written by Hanif D. Sherali and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.


A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems Related Books

A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems
Language: en
Pages: 529
Authors: Hanif D. Sherali
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problem
Nondifferentiable Optimization and Polynomial Problems
Language: en
Pages: 407
Authors: N.Z. Shor
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objecti
Duality Principles in Nonconvex Systems
Language: en
Pages: 476
Authors: David Yang Gao
Categories: Mathematics
Type: BOOK - Published: 2000-01-31 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, with
Mixed Integer Nonlinear Programming
Language: en
Pages: 687
Authors: Jon Lee
Categories: Mathematics
Type: BOOK - Published: 2011-12-02 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving
Foundations of Bilevel Programming
Language: en
Pages: 318
Authors: Stephan Dempe
Categories: Mathematics
Type: BOOK - Published: 2005-12-19 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part