The maximum concurrent flow problem
Journal of the ACM (JACM)
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
A Specialized Interior-Point Algorithm for Multicommodity Network Flows
SIAM Journal on Optimization
MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Solving Real-World Linear Programs: A Decade and More of Progress
Operations Research
Iterative algorithms for solving linear programs from engineering applications
Iterative algorithms for solving linear programs from engineering applications
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Dantzig-Wolfe and block coordinate-descent decomposition in large-scale integrated refinery-planning
Computers and Operations Research
Optimal admissible composition of abstraction heuristics
Artificial Intelligence
Automatic structure detection in constraints of tabular data
PSD'06 Proceedings of the 2006 CENEX-SDC project international conference on Privacy in Statistical Databases
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Multicommodity flows belong to the class of primal block-angular problems. An efficient interior-point method has already been developed for linear and quadratic network optimization problems. It solved normal equations, using sparse Cholesky factorizations for diagonal blocks, and a preconditioned conjugate gradient for linking constraints. In this work we extend this procedure, showing that the preconditioner initially developed for multicommodity flows applies to any primal block-angular problem, although its efficiency depends on each particular linking constraints structure. We discuss the conditions under which the preconditioner is effective. The procedure is implemented in a user-friendly package in the MATLAB environment. Computational results are reported for four primal block-angular problems: multicommodity flows, nonoriented multicommodity flows, minimum-distance controlled tabular adjustment for statistical data protection, and the minimum congestion problem. The results show that this procedure holds great potential for solving large primal-block angular problems efficiently.