Interior Point Methods for Linear Optimization

2. Auflage Softcover version of original hardcover Auflage 2005
ISBN: 978-1-4419-3887-9
Verlag: Springer US

Buch, Englisch, 497 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 785 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Roos, Cornelis

Vial, J. -Ph.

Terlaky, Tamás

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.