Ebook: Redundancy in Mathematical Programming: A State-of-the-Art Survey

During the Spring of 1979 one of us (Zionts) was invited to visit Erasmus University in Rotterdam, The Netherlands. It was there that Zionts met another of us (Telgen) who was then in the process of completing a dissertation on redundancy in linear programming. At that time, Telgen proposed an extended visit to Buffalo, during which time he and Zionts would do an extensive study on redundancy. Redundancy, hardly an exciting or new topic, does have numerous applications. Telgen and Zionts planned the project for the Summer of 1980, and enlisted the support of all the contributors as well as the other two members of our team (Karwan and Lotfi). Lotfi was then a Ph. D. student in Industrial Engineering searching for a thesis topic. Redundancy became his topic. Karwan and Zionts served as his thesis co-chairmen, with Telgen serving as an outside reader of the thesis. We initially had hoped to complete the study during Telgen's stay in Buffalo, but that was far too optimistic. Lotfi completed his dissertation during the late Spring-early Summer of 1981. As the project took shape, we decided that we had more than enough for an article, or even several articles. Accordingly, not wanting to produce redundant papers, we decided to produce this volume --- a state-of-the-art review of methods for handling redundancy and comprehensive tests of the various methods, together with extensions and further developments of the most promising methods.

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Content:
Front Matter....Pages N2-VII
An Introduction to Redundancy....Pages 1-13
Mathematical Foundations and Notation....Pages 14-27
A Method for Identifying Redundant Constraints and Extraneous Variables in Linear Programming....Pages 28-35
A Method for Determining Redundant Constraints....Pages 36-52
Identifying Redundancy in Systems of Linear Constraints....Pages 53-59
Finding Redundant Constraints in Sets of Linear Inequalities....Pages 60-67
A Method for Finding Redundant Constraints of a System of Linear Inequalities....Pages 68-79
Some Reduction of Linear Programs Using Bounds on Problem Variables....Pages 80-86
A Reduction Procedure for Linear and Integer Programming Models....Pages 87-107
Preduce — A Probabilistic Algorithm Identifying Redundancy by a Random Feasible Point Generator (RFPG)....Pages 108-134
The Noncandidate Constraint Method....Pages 135-144
Structural Redundancy in Large-Scale Optimization Models....Pages 145-169
Programming the Methods and Experimental Design....Pages 170-179
Results of the Sign Test Methods....Pages 180-207
Results of the Other Methods....Pages 208-233
Improvements and Extensions....Pages 234-251
Results of the Improvements and Extensions....Pages 252-275
Conclusions....Pages 276-278
Back Matter....Pages 279-289

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Content:
Front Matter....Pages N2-VII
An Introduction to Redundancy....Pages 1-13
Mathematical Foundations and Notation....Pages 14-27
A Method for Identifying Redundant Constraints and Extraneous Variables in Linear Programming....Pages 28-35
A Method for Determining Redundant Constraints....Pages 36-52
Identifying Redundancy in Systems of Linear Constraints....Pages 53-59
Finding Redundant Constraints in Sets of Linear Inequalities....Pages 60-67
A Method for Finding Redundant Constraints of a System of Linear Inequalities....Pages 68-79
Some Reduction of Linear Programs Using Bounds on Problem Variables....Pages 80-86
A Reduction Procedure for Linear and Integer Programming Models....Pages 87-107
Preduce — A Probabilistic Algorithm Identifying Redundancy by a Random Feasible Point Generator (RFPG)....Pages 108-134
The Noncandidate Constraint Method....Pages 135-144
Structural Redundancy in Large-Scale Optimization Models....Pages 145-169
Programming the Methods and Experimental Design....Pages 170-179
Results of the Sign Test Methods....Pages 180-207
Results of the Other Methods....Pages 208-233
Improvements and Extensions....Pages 234-251
Results of the Improvements and Extensions....Pages 252-275
Conclusions....Pages 276-278
Back Matter....Pages 279-289
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