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Interior Point Approach to Linear, Quadratic and Convex Programming : Algorithms and Complexity - D.den Hertog

Interior Point Approach to Linear, Quadratic and Convex Programming

Algorithms and Complexity

Hardcover Published: 31st March 1994
ISBN: 9780792327349
Number Of Pages: 210

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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. This text should be suitable 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.

`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

Glossary of symbols and notations
Introduction of IPMsp. 1
The logarithmic barrier methodp. 9
The center methodp. 73
Reducing the complexity for LPp. 111
Discussion of other IPMsp. 145
Summary, conclusions and recommendationsp. 169
App. A Self-concordance proofsp. 175
App. B General technical lemmasp. 187
Bibliographyp. 191
Indexp. 205
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792327349
ISBN-10: 0792327349
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 210
Published: 31st March 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.4 x 17.0  x 1.27
Weight (kg): 0.5