Interior point methods for linear optimization
著者
書誌事項
Interior point methods for linear optimization
Springer, c2006
2nd ed.
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
The era of interior point methods (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 offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
目次
List of figures.- List of tables.- Preface.- Acknowledgements.- Introduction.- I. Introdcution: Theory and Complexity.- Duality Theory for Linear Optimization.- A Polynomial Algorithm for the Self-dual Model.- Solving the Canonical Problem.- II. The Logatithmic Barrier Approach.- Preliminaries.- The Dual Logarithmic Barrier Method.- The Primal-Dual Logarithmic Barrier Method.- Initialization.- III. 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.- IV. 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.- Appendices.- Bibliography.- Author Index.- Subject Index.- Symbol Index.
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