Nonconvex Optimization and Its Applications

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

Authors: Sherali, Hanif D., Adams, W. P.

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About this book

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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $169.00
price for USA in USD
  • ISBN 978-1-4757-4388-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $299.99
price for USA in USD
  • ISBN 978-0-7923-5487-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $219.99
price for USA in USD
  • ISBN 978-1-4419-4808-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems
Authors
Series Title
Nonconvex Optimization and Its Applications
Series Volume
31
Copyright
1999
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4757-4388-3
DOI
10.1007/978-1-4757-4388-3
Hardcover ISBN
978-0-7923-5487-1
Softcover ISBN
978-1-4419-4808-3
Series ISSN
1571-568X
Edition Number
1
Number of Pages
XXIV, 518
Topics