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Partial table of contents: INTRODUCTION: THEORY AND COMPLEXITY. Duality Theory for Linear Optimization. A Polynomial Algorithm for the Skew-Symmetric Model. Solving the Canonical Problem. THE LOGARITHMIC BARRIER APPROACH. The Dual Logarithmic Barrier Method. Initialization. THE TARGET-FOLLOWING APPROACH. The Primal-Dual Newton Method. Application to the Method of Centers. MISCELLANEOUS TOPICS. Karmarkar's Projective Method. More Properties of the Central Path. Partial Updating. High-Order Methods. Parametric and Sensitivity Analysis. Implementing Interior Point Methods. Appendices. Bibliography. Indexes.