Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice

1. Front Matter

   Pages i-xix

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2. Early Algorithms

   Pages 1-25

3. The Exponential Potential Function - key Ideas

   Pages 27-49

4. Recent Developments

   Pages 51-72

5. Computational Experiments Using the Exponential Potential Function Framework

   Pages 73-110

6. Back Matter

   Pages 103-111

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Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.

• algorithms
• design
• linear optimization
• mathematical programming
• optimization
• programming

• Department of IEOR, Columbia University, New York

  Daniel Bienstock

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