A new polynomial-time algorithm for linear programming
Combinatorica
Primal-dual interior-point methods
Primal-dual interior-point methods
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Preconditioning indefinite systems in interior point methods for large scale linear optimisation
Optimization Methods & Software
Model-driven autotuning of sparse matrix-vector multiply on GPUs
Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
On the limits of GPU acceleration
HotPar'10 Proceedings of the 2nd USENIX conference on Hot topics in parallelism
Improving the Performance of the Sparse Matrix Vector Product with GPUs
CIT '10 Proceedings of the 2010 10th IEEE International Conference on Computer and Information Technology
Matrix-free interior point method
Computational Optimization and Applications
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The matrix-free technique is an iterative approach to interior point methods (IPM), so named because both the solution procedure and the computation of an appropriate preconditioner require only the results of the operations Ax and ATy, where A is the matrix of constraint coefficients. This paper demonstrates its overwhelmingly superior performance on two classes of linear programming (LP) problems relative to both the simplex method and to IPM with equations solved directly. It is shown that the reliance of this technique on sparse matrix-vector operations enables further, significant performance gains from the use of a GPU, and from multi-core processors.