Interior Point Algorithms: Theory And Analysis

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

The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool.

Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of the subject. Beginning with an overview of fundamental mathematical procedures, Professor Yinyu Ye moves swiftly on to in-depth explorations of numerous computational problems and the algorithms that have been developed to solve them. An indispensable text/reference for students and researchers in applied mathematics, computer science, operations research, management science, and engineering, Interior Point Algorithms:
* Derives various complexity results for linear and convex programming
* 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 nonlinear programming and nonconvex optimization.

YINYU YE, PhD, is Professor in the Department of Management Sciences at the University of Iowa College of Business Administration and the Program in Applied Mathematical & Computational Sciences.

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.