Dynamic Factorization in Large-Scale Optimization

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Authors
Brown, Gerald G.
Olson, Michael
Subjects
Factorization
Linear programming
Generalized upper bounds
Pure networks
Generalized networks
Advisors
Date of Issue
1994
Date
1994
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Abstract
Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generated from the remaining explicit part. Dynamic factorization admits algebraic elements which change in dimension during the course of solution. A unifying mathematical framework for dynamic row factorization is presented with three algorithms which derive from different LP model row structures: generalized upper bound rows, pure network rows,and generalized network TOWS. Each of these structures is a generalization of its predecessors, and each corresponding algorithm exhibits just enough additional richness to accommodate the structure at hand within the unified framework. Implementation and computational results are presented for a variety of real-world models. These results suggest that each of these algorithms is superior to the traditional, non-factorized approach, with the degree of improvement depending upon the size and quality of the row factorization identified.
Type
Article
Description
Mathematical Programming, 64, pp. 17-51.
URI
https://hdl.handle.net/10945/38133
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Operations Research (OR)
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Citation
Brown, G.G. and Olson, M., 1994, “Dynamic Factorization in Large-Scale Optimization,” Mathematical Programming, 64, pp. 17-51.
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defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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