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Applied Optimization

Interior Point Methods of Mathematical Programming

Editors: Terlaky, Tamas (Ed.)

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About this book

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every­ body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro­ gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin­ cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob­ lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).

Table of contents (13 chapters)

  • Introduction to the Theory of Interior Point Methods

    Jansen, Benjamin (et al.)

    Pages 3-34

  • Affine Scaling Algorithm

    Tsuchiya, Takashi

    Pages 35-82

  • Target-Following Methods for Linear Programming

    Jansen, Benjamin (et al.)

    Pages 83-124

  • Potential Reduction Algorithms

    Anstreicher, Kurt M.

    Pages 125-158

  • Infeasible-Interior-Point Algorithms

    Mizuno, Shinji

    Pages 159-187

Buy this book

eBook $349.00
price for USA (gross)
  • ISBN 978-1-4613-3449-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $449.00
price for USA
  • ISBN 978-0-7923-4201-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $449.00
price for USA
  • ISBN 978-1-4613-3451-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Interior Point Methods of Mathematical Programming
Editors
  • Tamas Terlaky
Series Title
Applied Optimization
Series Volume
5
Copyright
1996
Publisher
Springer US
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-1-4613-3449-1
DOI
10.1007/978-1-4613-3449-1
Hardcover ISBN
978-0-7923-4201-4
Softcover ISBN
978-1-4613-3451-4
Series ISSN
1384-6485
Edition Number
1
Number of Pages
XXII, 530
Topics