Vector processing in simplex and interior methods for linear programming

DOI10.1007/BF02023049zbMath0714.90064OpenAlexW2079547145MaRDI QIDQ751499

D. Kharzeev

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1007/bf02023049

zbMATH Keywords

simplex methodinterior point methods

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Linear programming (90C05) Computational methods for problems pertaining to operations research and mathematical programming (90-08) Distributed algorithms (68W15)

Related Items

On the efficacy of distributed simplex algorithms for linear programming ⋮ Implementing cholesky factorization for interior point methods of linear programming ⋮ Towards a practical parallelisation of the simplex method ⋮ Steepest-edge simplex algorithms for linear programming ⋮ The most-obtuse-angle row pivot rule for achieving dual feasibility: A computational study ⋮ Advances in design and implementation of optimization software ⋮ Massive memory buys little speed for complete, in-core sparse Cholesky factorizations on some scalar computers

Uses Software

• LSQR
• DEVEX
• symrcm
• CRAIG

Cites Work

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• A new polynomial-time algorithm for linear programming
• Parallel implementation of multifrontal schemes
• Relaxed variants of Karmarkar's algorithm for linear programs with unknown optimal objective value
• An implementation of Karmarkar's algorithm for linear programming
• Evolution of Linear Programming Computing Techniques
• On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method
• Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine
• The Multifrontal Solution of Indefinite Sparse Symmetric Linear
• The Use of BLAS3 in Linear Algebra on a Parallel Processor with a Hierarchical Memory
• The Impact of Hardware Gather/Scatter on Sparse Gaussian Elimination
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases
• An Implementation of a Primal-Dual Interior Point Method for Linear Programming
• Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm
• 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
• Symbolic Generation of an Optimal Crout Algorithm for Sparse Systems of Linear Equations
• Pivot selection methods of the Devex LP code

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