Interior Point Methods for Linear Optimization

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Springer Science & Business Media, Sep 7, 2005 - Mathematics - 497 pages
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.
 

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Contents

Theory and Complexity
13
The Logarithmic Barrier Approach
85
The PrimalDual Logarithmic Barrier Method 149
148
Initialization
213
The PrimalDual Newton Method
235
Applications 247
246
The Dual Newton Method
259
The Primal Newton Method
269
Partial Updating
317
HigherOrder Methods
329
Parametric and Sensitivity Analysis
361
Implementing Interior Point Methods 401
400
Appendix A Some Results from Analysis
431
Transformation to canonical form
445
Appendix E The Dikin step algorithm
451
Bibliography 461
460

Application to the Method of Centers
277
Karmarkars Projective Method
289
More Properties of the Central Path 307
306

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