Interior Point Approach to Linear, Quadratic and Convex Programming: Algorithms and Complexity

✍ Scribed by D. den Hertog (auth.)

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Leaves: 213
• Series: Mathematics and Its Applications 277
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction of IPMs....Pages 1-8
The logarithmic barrier method....Pages 9-71
The center method....Pages 73-109
Reducing the complexity for LP....Pages 111-143
Discussion of other IPMs....Pages 145-167
Summary, conclusions and recommendations....Pages 169-173
Back Matter....Pages 175-210

✦ Subjects

Optimization; Algorithms; Theory of Computation; Convex and Discrete Geometry; Numeric Computing