Nonconvex Optimization and Its Applications

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Theory, Algorithms, Software, and Applications

Authors: Tawarmalani, Mohit, Sahinidis, Nikolaos

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About this book

Interest in constrained optimization originated with the simple linear pro­ gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re­ visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de­ velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter­ ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Table of contents (11 chapters)

  • Introduction

    Tawarmalani, Mohit (et al.)

    Pages 1-23

  • Convex Extensions and Relaxation Strategies

    Tawarmalani, Mohit (et al.)

    Pages 25-70

  • Product Disaggregation in Global Optimization and Relaxations of Rational Programs

    Tawarmalani, Mohit (et al.)

    Pages 71-123

  • Relaxations of Factorable Programs

    Tawarmalani, Mohit (et al.)

    Pages 125-145

  • Domain Reduction

    Tawarmalani, Mohit (et al.)

    Pages 147-187

Buy this book

eBook $259.00
price for USA (gross)
  • ISBN 978-1-4757-3532-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $329.00
price for USA
  • ISBN 978-1-4020-1031-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $329.00
price for USA
  • ISBN 978-1-4419-5235-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
Book Subtitle
Theory, Algorithms, Software, and Applications
Authors
Series Title
Nonconvex Optimization and Its Applications
Series Volume
65
Copyright
2002
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4757-3532-1
DOI
10.1007/978-1-4757-3532-1
Hardcover ISBN
978-1-4020-1031-6
Softcover ISBN
978-1-4419-5235-6
Series ISSN
1571-568X
Edition Number
1
Number of Pages
XXV, 478
Number of Illustrations and Tables
89 b/w illustrations
Topics