Advertisement

Interior Point Approach to Linear, Quadratic and Convex Programming

Algorithms and Complexity

  • D. den Hertog

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. D. den Hertog
    Pages 1-8
  3. D. den Hertog
    Pages 9-71
  4. D. den Hertog
    Pages 73-109
  5. D. den Hertog
    Pages 111-143
  6. D. den Hertog
    Pages 145-167
  7. D. den Hertog
    Pages 169-173
  8. Back Matter
    Pages 175-210

About this book

Introduction

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.

Keywords

Mathematica Notation Optimum algorithms complexity linear optimization optimization programming quadratic programming

Authors and affiliations

  • D. den Hertog
    • 1
  1. 1.Centre for Quantative MethodsEindhovenThe Netherlands

Bibliographic information

Industry Sectors
Pharma
Biotechnology
Finance, Business & Banking
Electronics
IT & Software
Energy, Utilities & Environment