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Interior Point Algorithms: Theory and Analysis

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Interior Point Algorithms: Theory and Analysis

Yinyu Ye

ISBN: 978-1-118-03095-0 October 2011 440 Pages

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Description

The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques.

The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool.

Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms:
* Derives various complexity results for linear and convexprogramming
* Emphasizes interior point geometry and potential theory
* Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques
* Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.
Geometry of Convex Inequalities.

Computation of Analytic Center.

Linear Programming Algorithms.

Worst-Case Analysis.

Average-Case Analysis.

Asymptotic Analysis.

Convex Optimization.

Nonconvex Optimization.

Implementation Issues.

Bibliography.

Index.