Theory of linear and integer programming
Theory of linear and integer programming
Pathways to the optimal set in linear programming
on Progress in Mathematical Programming: Interior-Point and Related Methods
A primal-dual infeasible-interior-point algorithm for linear programming
Mathematical Programming: Series A and B
Iterative solution methods
An Investigation of Interior-Point Algorithms for the Linear Transportation Problem
SIAM Journal on Scientific Computing
Primal-dual interior-point methods
Primal-dual interior-point methods
Network Flows and Matching: First DIMACS Implementation Challenge
Network Flows and Matching: First DIMACS Implementation Challenge
Modified Cholesky Factorizations in Interior-Point Algorithms for Linear Programming
SIAM Journal on Optimization
A reduced dual affine scaling algorithm for solving assignment and transportation problems
A reduced dual affine scaling algorithm for solving assignment and transportation problems
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
Experiments with a hybrid interior point/combinatorial approach for network flow problems
Optimization Methods & Software
A stable primal---dual approach for linear programming under nondegeneracy assumptions
Computational Optimization and Applications
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We study and compare preconditioners available for network interior point methods. We derive upper bounds for the condition number of the preconditioned matrices used in the solution of systems of linear equations defining the algorithm search directions. The preconditioners are tested using PDNET, a state-of-the-art interior point code for the minimum cost network flow problem. A computational comparison using a set of standard problems improves the understanding of the effectiveness of preconditioners in network interior point methods.