Network Flows Heuristics for Complementary Cell Suppression: An Empirical Evaluation and Extensions
Inference Control in Statistical Databases, From Theory to Practice
A Parallel Implementation of an Interior-Point Algorithm for Multicommodity Network Flows
VECPAR '00 Selected Papers and Invited Talks from the 4th International Conference on Vector and Parallel Processing
An Augmented Lagrangian Algorithm for Large Scale Multicommodity Routing
Computational Optimization and Applications
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Prim-based support-graph preconditioners for min-cost flow problems
Computational Optimization and Applications
An interior-point approach for primal block-angular problems
Computational Optimization and Applications
Experiments with a hybrid interior point/combinatorial approach for network flow problems
Optimization Methods & Software
Dantzig-Wolfe and block coordinate-descent decomposition in large-scale integrated refinery-planning
Computers and Operations Research
A Parallel Algorithm for NMNF Problems with a Large Number of Capacity Constraints
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A linear model for compound multicommodity network flow problems
Computers and Operations Research
Optimization of a statically partitioned hypermatrix sparse cholesky factorization
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Existence, uniqueness, and convergence of the regularized primal-dual central path
Operations Research Letters
A preconditioning technique for Schur complement systems arising in stochastic optimization
Computational Optimization and Applications
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Despite the efficiency shown by interior-point methods in large-scale linear programming, they usually perform poorly when applied to multicommodity flow problems. The new specialized interior-point algorithm presented here overcomes this drawback. This specialization uses both a preconditioned conjugate gradient solver and a sparse Cholesky factorization to solve a linear system of equations at each iteration of the algorithm. The ad hoc preconditioner developed by exploiting the structure of the problem is instrumental in ensuring the efficiency of the method. An implementation of the algorithm is compared to state-of-the-art packages for multicommodity flows. The computational experiments were carried out using an extensive set of test problems, with sizes of up to 700,000 variables and 150,000 constraints. The results show the effectiveness of the algorithm.