Skip to main content
SpringerLink
Log in

Interior Point Methods of Mathematical Programming

  • Book
  • © 1996

Overview

Editors:
  1. Tamás Terlaky

    1. Delft University of Technology, The Netherlands

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxi
    Download chapter PDF

  2. Linear Programming

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction to the Theory of Interior Point Methods

      • Benjamin Jansen, Cornelis Roos, Tamás Terlaky
      Pages 3-34

    3. Affine Scaling Algorithm

      • Takashi Tsuchiya
      Pages 35-82

    4. Target-Following Methods for Linear Programming

      • Benjamin Jansen, Cornelis Roos, Tamás Terlaky
      Pages 83-124

    5. Potential Reduction Algorithms

      • Kurt M. Anstreicher
      Pages 125-158

    6. Infeasible-Interior-Point Algorithms

      • Shinji Mizuno
      Pages 159-187

    7. Implementation of Interior-Point Methods for Large Scale Linear Programs

      • Erling D. Anderson, Jacek Gondzio, Csaba Mészáros, Xiaojie Xu
      Pages 189-252

  3. Convex Programming

    1. Front Matter

      Pages 253-253
      Download chapter PDF

    2. Interior-Point Methods for Classes of Convex Programs

      • Florian Jarre
      Pages 255-296

    3. Complementarity Problems

      • Akiko Yoshise
      Pages 297-367

    4. Semidefinite Programming

      • Motakuri V. Ramana, Panos M. Pardalos
      Pages 369-398

    5. Implementing Barrier Methods for Nonlinear Programming

      • David F. Shanno, Mark G. Breitfeld, Evangelia M. Simantiraki
      Pages 399-414

  4. Applications, Extensions

    1. Front Matter

      Pages 415-415
      Download chapter PDF

    2. Interior Point Methods for Combinatorial Optimization

      • John E. Mitchell
      Pages 417-466

    3. Interior Point Methods for Global Optimization

      • Panos M. Pardalos, Mauricio G. C. Resende
      Pages 467-500

    4. Interior Point Approaches for the VLSI Placement Problem

      • Anthony Vannelli, Andrew Kennings, Paulina Chin
      Pages 501-528
Back to top

Keywords

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).

Editors and Affiliations

  • Delft University of Technology, The Netherlands

    Tamás Terlaky

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation