Interior Point Methods For Linear Optimization: Second Edition

Hardcover | September 7, 2005

byCornelis Roos, Tamas Terlaky, J.-Ph. Vial

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The era of interior point methods (IPMs) was initiated by N. Karmarkar's 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.

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From the Publisher

The era of interior point methods (IPMs) was initiated by N. Karmarkar's 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises a...

From the Jacket

Linear Optimization (LO) is one of the most widely applied and taught techniques in mathematics, with applications in many areas of science, commerce and industry. The dramatically increased interest in the subject is due mainly to advances in computer technology and the development of Interior Point Methods (IPMs) for LO.This book pro...

Format:HardcoverDimensions:521 pages, 9.25 × 6.1 × 0 inPublished:September 7, 2005Publisher:Springer USLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387263780

ISBN - 13:9780387263786

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Table of Contents

List of figures.- List of tables.- Preface.- Acknowledgements.- Introduction.- I. Introdcution: Theory and Complexity.- Duality Theory for Linear Optimization.- A Polynomial Algorithm for the Self-dual Model.- Solving the Canonical Problem.- II. The Logatithmic Barrier Approach.- Preliminaries.- The Dual Logarithmic Barrier Method.- The Primal-Dual Logarithmic Barrier Method.- Initialization.- III. The Target-Following Approach.- Preliminaries.- The Primal-Dual Newton Method.- Applications.- The Dual Newton Method.- The Primal Newton Method.- Application to the Method of Centers.- IV. Miscellaneous Topics.- Karmarkar's Projective Method.- More Properties of the Central Path.- Partial Updating.- Higher-Order Methods.- Parametric and Sensitivity Analysis.- Implementing Interior Point Methods.- Appendices.- Bibliography.- Author Index.- Subject Index.- Symbol Index.

Editorial Reviews

From the reviews of the second edition:"The second edition of this successful book on interior point methods for linear optimization appears eight years after the first one. It presents a unified framework for these algorithms and it is a comprehensive treatment of linear optimization from the perspective of interior point methods. . The presentation is clear and comprehensible, but concise, it comes along with many examples and illustrations . . Almost all aspects of interior point methods are discussed in this highly recommendable book . ." (Petra Huhn, Mathematical Methods of Operations Research, Vol. 65 (1), 2007)