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Interior Point Approach to Linear, Quadratic and Convex Programming

Algorithms and Complexity

  • Book
  • © 1994

Overview

Authors:
  1. D. Hertog

    1. Centre for Quantative Methods, Eindhoven, The Netherlands

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Part of the book series: Mathematics and Its Applications (MAIA, volume 277)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction of IPMs

    • D. den Hertog
    Pages 1-8

  3. The logarithmic barrier method

    • D. den Hertog
    Pages 9-71

  4. The center method

    • D. den Hertog
    Pages 73-109

  5. Reducing the complexity for LP

    • D. den Hertog
    Pages 111-143

  6. Discussion of other IPMs

    • D. den Hertog
    Pages 145-167

  7. Summary, conclusions and recommendations

    • D. den Hertog
    Pages 169-173

  8. Back Matter

    Pages 175-210
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Keywords

About this book

This book describes the rapidly developing field of interior point methods (IPMs). An extensive analysis is given of path-following methods for linear programming, quadratic programming and convex programming. These methods, which form a subclass of interior point methods, follow the central path, which is an analytic curve defined by the problem. Relatively simple and elegant proofs for polynomiality are given. The theory is illustrated using several explicit examples. Moreover, an overview of other classes of IPMs is given. It is shown that all these methods rely on the same notion as the path-following methods: all these methods use the central path implicitly or explicitly as a reference path to go to the optimum.
For specialists in IPMs as well as those seeking an introduction to IPMs. The book is accessible to any mathematician with basic mathematical programming knowledge.

Reviews

`This book presents a general and rigorous foundation for solving nonlinear convex optimization problems. The book is well and clearly written. It is comprehensive and well-balanced ... excellent text for an advanced or seminar course on optimization, primarily addressed to graduate students in mathematics, pure or applied, computer science and engineering schools. ... researchers will also find it a valuable reference because the theorems contained in many of its sections represent the current state of the art. ... extensive bibliographic section is another strong point of the book, quite complete and up to date. I believe this work will remain a basic reference for whomever is interested in convex optimization for years to come. '
Optima, 47, 1995

Authors and Affiliations

  • Centre for Quantative Methods, Eindhoven, The Netherlands

    D. Hertog

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