A projective simplex algorithm using LU decomposition

DOI10.1016/S0898-1221(99)00323-5zbMath0974.90013MaRDI QIDQ1975340

Ping-Qi Pan

Publication date: 15 July 2001

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

linear programmingsimplex algorithmLU decomposition

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Decomposition methods (49M27)

Related Items

A phase-1 approach for the generalized simplex algorithm ⋮ Efficient nested pricing in the simplex algorithm ⋮ A primal deficient-basis simplex algorithm for linear programming ⋮ A variant of the dual face algorithm using Gauss-Jordan elimination for linear programming ⋮ An affine-scaling pivot algorithm for linear programming

Uses Software

• DEVEX
• NETLIB LP Test Set

Cites Work

• Practical finite pivoting rules for the simplex method
• A dual approach to primal degeneracy
• A projective simplex method for linear programming
• A dual projective simplex method for linear programming
• The economical storage of plane rotations
• The most-obtuse-angle row pivot rule for achieving dual feasibility: A computational study
• Pivot rules for linear programming: A survey on recent theoretical developments
• The simplex algorithm with a new primal and dual pivot rule
• Investigating the sparse simplex algorithm on a distributed memory multiprocessor
• Steepest-edge simplex algorithms for linear programming
• A basis-defiency-allowing variation of the simplex method for linear programming
• Numerical methods for solving linear least squares problems
• A stabilization of the simplex method
• The Criss-Cross Method for Solving Linear Programming Problems
• Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form
• A convergent criss-cross method
• A practicable steepest-edge simplex algorithm
• A simplex-like method with bisection for linear programming¹
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results
• A Variant of the Dual Pivoting Rule in Linear Programming
• Updated triangular factors of the basis to maintain sparsity in the product form simplex method
• Methods for Modifying Matrix Factorizations
• Inductive Proof of the Simplex Method
• The simplex method of linear programming using LU decomposition
• Pivot selection methods of the Devex LP code
• The Product Form for the Inverse in the Simplex Method
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