Presolve analysis of linear programs prior to applying the interior point method
Several issues concerning an analysis of large and sparse linear programming problems prior to solving them with an interior point based optimizer are addressed in this talk. Three types of presolve procedures are distinguished. Routines from the first class repeatedly analyse an LP problem formulation: eliminate empty or singleton rows and columns, look for primal and dual forcing or dominated constraints, tighten bounds for variables and shadow prices or just the opposite, relax them to find implied free variables. The second type of analysis aims at reducing a fill-in of a Cholesky factor of normal equations matrix used to compute Karmarkar`s projections and include a heuristic for increasing a sparsity of the LP constraint matrix and a technique of splitting dense columns in it. Finally, routines from the third class detect and remove different linear dependencies (of rows and columns) in a constraint matrix. Computational results on problems from the Netlib collection (including recently added infeasible ones) are given. For feasible problems, the use of presolve procedure results in a significant reduction of the following solution time. If the linear program is infeasible, its status often (in 15 of 29 cases, as our experience shows) can be determined during the presolve analysis.
- OSTI ID:
- 36076
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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