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!

  • $\begingroup$ When you say linear problem, do you mean linear objective function and linear constraints? $\endgroup$ Commented Aug 6, 2014 at 14:03
  • $\begingroup$ And in general, do consider commercial or free solver? $\endgroup$ Commented Aug 6, 2014 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
    Commented Aug 10, 2014 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! $\endgroup$ Commented Aug 11, 2014 at 5:46


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