Browsing by Author "Lustig, Irvin J."

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    An Implementation of a Parallel Primal-Dual Interior Point Method for Multicommodity Flow Problems
    (1992-01) Li, Guangye; Lustig, Irvin J.
    An implementation of the primal-dual predictor-corrector interior point method is specialized to solve linear multicommodity flow problems. The block structure of the constraint matrix is exploited via parallel computation. The bundling constraints require the Cholesky factorization of a dense matrix, where a method that exploits parallelism for the dense Cholesky factorization is used. The resulting implementation is 65 to 90 percent efficient, depending on the problem instance. For a problem with K commodities, an approximate speedup for the interior point method of 0.8K is realized.
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    Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods
    (1991-05) Bixby, Robert E.; Gregory, John W.; Lustig, Irvin J.; Marsten, Roy E.; Shanno, David F.
    Experience with solving a 12,753,313 variable linear program is described. This problem is the linear programming relaxation of a set partitioning problem arising from an airline crew scheduling application. A scheme is described that requires successive solutions of small subproblems, yielding a procedure that has little growth in solution time in terms of the number of variables. Experience using the simplex method as implemented in CPLEX, an interior point method as implemented in OB1, and hybrid interior point/simplex approach is reported. The resulting procedure illustrates the power of an interior point/simplex combination for solving very large-scale linear programs.