A fast LU update for linear programming

DOI10.1007/BF02025534zbMath0784.90049OpenAlexW1978917746MaRDI QIDQ1309856

Leena M. Suhl, Uwe H. Suhl

Publication date: 21 March 1994

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02025534

zbMATH Keywords

simplex-based linear programming softwaresparse matrix kernels

Mathematics Subject Classification ID

Linear programming (90C05) Computational methods for problems pertaining to operations research and mathematical programming (90-08)

Related Items (15)

Numerical aspects in developing LP softwares, LPAKO and LPABO ⋮ Supernode processing of mixed-integer models ⋮ Progress in the dual simplex method for large scale LP problems: Practical dual phase 1 algorithms ⋮ Parallel distributed-memory simplex for large-scale stochastic LP problems ⋮ A nearly optimal randomized algorithm for explorable heap selection ⋮ Roundoff-Error-Free Basis Updates of LU Factorizations for the Efficient Validation of Optimality Certificates ⋮ Permutations in the Factorization of Simplex Bases ⋮ Improving a primal–dual simplex-type algorithm using interior point methods ⋮ The double pivot simplex method ⋮ A survey of direct methods for sparse linear systems ⋮ Sparsity of integer formulations for binary programs ⋮ On a dual method for a specially structured linear programming problem with application to stochastic programming ⋮ LPAKO: A Simplex-based Linear Programming Program ⋮ Progress in the dual simplex algorithm for solving large scale LP problems: Techniques for a fast and stable implementation ⋮ Novel update techniques for the revised simplex method

Uses Software

• MOPS
• OSL

Cites Work

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• Solving staircase linear programs by the simplex method, 1: Inversion
• A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases
• Computing Sparse LU Factorizations for Large-Scale Linear Programming Bases
• The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results
• Updated triangular factors of the basis to maintain sparsity in the product form simplex method
• The simplex method of linear programming using LU decomposition

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