Interior Point Methods for Linear Optimization

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)

• 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.