Mathematics and Its Applications

Algorithms and Complexity

By: D. Den Hertog

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Hardcover | 31 March 1994

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Hardcover
228 Pages

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25.4 x 17.15 x 1.27

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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.
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.

Industry 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

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Mathematical Theory of Computation Mathematics Optimisation Linear Programming Geometry Analytic Geometry Applied Mathematics Mathematical Modelling Computer Programming & Software Development

Algorithms & Data Structures Calculus & Mathematical Analysis Numerical Analysis

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Paperback

Published: 10th October 2012

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Glossary of symbols and notations
Introduction of IPMs	p. 1
The logarithmic barrier method	p. 9
The center method	p. 73
Reducing the complexity for LP	p. 111
Discussion of other IPMs	p. 145
Summary, conclusions and recommendations	p. 169
App. A Self-concordance proofs	p. 175
App. B General technical lemmas	p. 187
Bibliography	p. 191
Index	p. 205
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

Algorithms and Complexity

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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