A practical anti-cycling procedure for linearly constrained optimization
Mathematical Programming: Series A and B
Steepest-edge simplex algorithms for linear programming
Mathematical Programming: Series A and B
The Dual Active Set Algorithm and Its Application to Linear Programming
Computational Optimization and Applications
MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Parallelizing the Dual Simplex Method
INFORMS Journal on Computing
Solving Real-World Linear Programs: A Decade and More of Progress
Operations Research
Computational Techniques of the Simplex Method
Computational Techniques of the Simplex Method
A Dual Projective Pivot Algorithm for Linear Programming
Computational Optimization and Applications
Hyper-Sparsity in the Revised Simplex Method and How to Exploit it
Computational Optimization and Applications
Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms
Computational Optimization and Applications
A sparse proximal implementation of the LP dual active set algorithm
Mathematical Programming: Series A and B
On the sparseness of 1-norm support vector machines
Neural Networks
A high performance dual revised simplex solver
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
Parallel distributed-memory simplex for large-scale stochastic LP problems
Computational Optimization and Applications
Implementing the simplex method as a cutting-plane method, with a view to regularization
Computational Optimization and Applications
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During the last fifteen years the dual simplex method has become a strong contender in solving large scale LP problems. However, the lack of descriptions of important implementation details in the research literature has led to a great performance gap between open-source research codes and commercial LP-systems. In this paper we present the mathematical algorithms, computational techniques and implementation details, which are the key factors for our dual simplex code to close this gap. We describe how to exploit hyper-sparsity in the dual simplex algorithm. Furthermore, we give a conceptual integration of Harris' ratio test, bound flipping and cost shifting techniques and describe a sophisticated and efficient implementation. We also address important issues of the implementation of dual steepest edge pricing. Finally we show on a large set of practical large scale LP problems, that our dual simplex code outperforms the best existing open-source and research codes and is competitive to the leading commercial LP-systems on our most difficult test problems.