Dynamic Factorization in Large-Scale Optimization
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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Factorization is an approach to linear programming LP in which the algebraic elements of the LP tableau are organized in such a way that a large portion of the tableau may be represented implicitly and generated from the remaining explicit part. In dynamic row factorization, the row structure of the LP model instance influences the algebraic structure of the tableau, and the dimension of the algebraic elements may change as the solution progresses. We present three algorithms motivated by this approach, each resulting from a different LPL model row structure generalized upper bound GUB rows, pure network rows and generalized network rows. We describe implementations of all three algorithms, specifying data structures for tableau and basis inverse representations and detailing procedures for manipulation and update of these representations.
- Operations Research