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I have a linear problem with a sparse, psd and strictly diagonally dominant matrix. Can you please point me to some known best solvers (in terms of runtime, or easy to be practically optimized for multicore and SIMD system)?

Currently my direction was to try conjugate gradient method, and it seems to solve the problem in about 8-10 iterations (for specific use case), which is pretty good. However I wonder if there are other solvers that take the advantages of those characteristics even better.

Much thanks!

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  • $\begingroup$ When you say linear problem, do you mean linear objective function and linear constraints? $\endgroup$ – AndreaCassioli Aug 6 '14 at 14:03
  • $\begingroup$ And in general, do consider commercial or free solver? $\endgroup$ – AndreaCassioli Aug 6 '14 at 14:03
  • $\begingroup$ @AC_MOSEK - yes, exactly. linear objective function and a set of linear constraints. Commercial solvers can be applied. Thanks! $\endgroup$ – rursw1 Aug 10 '14 at 13:04
  • $\begingroup$ I would say that there are no advantages you can take from the problem structure, except for sparsity, afaik. Sparsity is usually exploited by every decent LP solver. Please do not use gradient base method in this case! $\endgroup$ – AndreaCassioli Aug 11 '14 at 5:46

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