Dynamic factorization in large-scale optimization

Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generatedfrom the remainingexplicit part. Dynamicfactorization admits algebraicelementswhichchangeindimensionduring the courseof solution.A unifyingmathematical framework for dynamic row factorization is presented with three algorithms which derive from differentLP modelrowstructures:generalizedupperboundrows,purenetworkrows,and generalized networkTOWS. Eachof these structuresis a generalization of its predecessors, andeach corresponding algorithm exhibits just enough additional richness to accommodate the structure at hand within the unifledframework. Implementation andcomputational results arepresentedfor a varietyof real-world models. Theseresultssuggestthateachof thesealgorithmsis superiorto the traditional, non-factorized approach, with thedegreeof improvement dependingupon thesizeandqualityof the rowfactorization identified.