Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice
Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice (International Series in Operations Research & Management Science): : Daniel Bienstock
Springer | ISBN: 1402071736 | 2002 | PDF (OCR) | 110 pages | 4.86 Mb
Breaks ground in linear programming theory. Draws on the research developments in the areas of linear and integer programming, numerical analysis, and high-level algorithm design.
Table of Contents
List of Figures
List of Tables
Preface
1 Introduction
1 Early Algorithms 1
1 The Flow Deviation Method 3
2 The Shahrokhi and Matula Algorithm 13
2 The Exponential Potential Function - Key Ideas 27
1 A basic algorithm for min-max LPs 30
2 Round-robin and randomized schemes for block-angular problems 39
3 Optimization and more general feasibility systems 44
4 Width, revisited 47
5 Alternative potential functions 48
6 A philosophical point: why these algorithms are useful 48
3 Recent Developments 51
1 Oblivious rounding 51
2 Lower bounds for Frank-Wolfe methods 62
3 The algorithms of Garg-Konemann and Fleischer 66
4 Lagrangian Relaxation, Non-Differentiable Optimization and Penalty Methods 69
4 Computational Experiments 73
1 Basic Issues 78
2 Improving Lagrangian Relaxations 83
3 Restricted Linear Programs 86
4 Tightening formulations 88
5 Computational tests 89
6 Future work 101
App.: Frequency Asked Questions 103
References 107
Index 111
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