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Interior Point Methods for Linear Optimization is a comprehensive, thorough textbook on interior point methods (IPMs). The era of 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 gives a comprehensive review of the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
List of contents
Introduction: Theory and Complexity.- Duality Theory for Linear Optimization.- A Polynomial Algorithm for the Self-dual Model.- Solving the Canonical Problem.- The Logarithmic Barrier Approach.- Preliminaries.- The Dual Logarithmic Barrier Method.- The Primal-Dual Logarithmic Barrier Method.- Initialization.- 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.- 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.
Summary
Interior Point Methods for Linear Optimization is a comprehensive, thorough textbook on interior point methods (IPMs). The era of 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 gives a comprehensive review of the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
Additional text
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)
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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)
