A bump triangular dynamic factorization algorithm for the simplex method

DOI10.1007/BF01588296zbMath0428.90039MaRDI QIDQ3865837

Richard D. McBride

Publication date: 1980

Published in: Mathematical Programming (Search for Journal in Brave)

zbMATH Keywords

sparse matricessimplex methodcomputational experiencecomparison of algorithmslarge- scale linear programmingpartitioning methodsbump triangular dynamic factorization algorithmtriangular factorization of the basis

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Linear programming (90C05) Specification and verification (program logics, model checking, etc.) (68Q60)

Related Items (7)

Dynamic factorization in large-scale optimization ⋮ A Hierarchical Representation of the Inverse for Sparse Matrices ⋮ A warm-start dual simplex solution algorithm for the minimum flow networks with postoptimality analyses ⋮ Large-scale linear programming: Geometry, working bases and factorizations ⋮ A comprehensive simplex-like algorithm for network optimization and perturbation analysis ⋮ A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases ⋮ Implementation of a Double-Basis Simplex Method for the General Linear Programming Problem

Uses Software

• DEVEX

Cites Work

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• A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases
• The factorization approach to large-scale linear programming
• Matrix augmentation and partitioning in the updating of the basis inverse
• A Spike Collective Dynamic Factorization Algorithm for the Simplex Method
• Updated triangular factors of the basis to maintain sparsity in the product form simplex method
• A complete constructive algorithm for the general mixed linear programming problem
• The simplex method of linear programming using LU decomposition
• Reinversion with the preassigned pivot procedure
• Pivot selection methods of the Devex LP code

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