Advertisement

Interior Point Methods of Mathematical Programming

  • Tamás Terlaky

Part of the Applied Optimization book series (APOP, volume 5)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Linear Programming

    1. Front Matter
      Pages 1-1
    2. Benjamin Jansen, Cornelis Roos, Tamás Terlaky
      Pages 3-34
    3. Takashi Tsuchiya
      Pages 35-82
    4. Benjamin Jansen, Cornelis Roos, Tamás Terlaky
      Pages 83-124
    5. Kurt M. Anstreicher
      Pages 125-158
    6. Shinji Mizuno
      Pages 159-187
    7. Erling D. Anderson, Jacek Gondzio, Csaba Mészáros, Xiaojie Xu
      Pages 189-252
  3. Convex Programming

    1. Front Matter
      Pages 253-253
    2. Akiko Yoshise
      Pages 297-367
    3. Motakuri V. Ramana, Panos M. Pardalos
      Pages 369-398
    4. David F. Shanno, Mark G. Breitfeld, Evangelia M. Simantiraki
      Pages 399-414
  4. Applications, Extensions

    1. Front Matter
      Pages 415-415
    2. Panos M. Pardalos, Mauricio G. C. Resende
      Pages 467-500
    3. Anthony Vannelli, Andrew Kennings, Paulina Chin
      Pages 501-528

About this book

Introduction

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).

Keywords

algorithms combinatorial optimization complementarity complexity global optimization linear optimization Mathematica mathematical programming nonlinear optimization optimization Potential programming VLSI

Editors and affiliations

  • Tamás Terlaky
    • 1
  1. 1.Delft University of TechnologyThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-3449-1
  • Copyright Information Springer-Verlag US 1996
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-3451-4
  • Online ISBN 978-1-4613-3449-1
  • Series Print ISSN 1384-6485
  • Buy this book on publisher's site