<p>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)?</p>

<p>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. </p>

<p>Much thanks! </p>

CC BY-SA 3.0
2014-08-06T14:03:01.693Z
When you say linear problem, do you mean linear objective function and linear constraints?
AndreaCassioli
CC BY-SA 3.0
2014-08-06T14:03:35.187Z
And in general, do consider commercial or free solver?
AndreaCassioli
CC BY-SA 3.0
2014-08-10T13:04:05.983Z
@AC_MOSEK - yes, exactly. linear objective function and a set of linear constraints. Commercial solvers can be applied. Thanks!
rursw1
CC BY-SA 3.0
2014-08-11T05:46:39.190Z
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!
AndreaCassioli
<optimization><linear-programming><convex-optimization><sparse-matrix>
LP solver for sparse, PSD and strictly diagonally dominant matrix
rursw1
# LP solver for sparse, PSD and strictly diagonally dominant matrix

(Asked by: username_0 on 2014-08-06)

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!

**Tags:** optimization, linear-programming, convex-optimization, sparse-matrix

> **Comments:**
> **username_1**: When you say linear problem, do you mean linear objective function and linear constraints?  
> **username_1**: And in general, do consider commercial or free solver?  
> **username_0**: @AC_MOSEK - yes, exactly. linear objective function and a set of linear constraints. Commercial solvers can be applied. Thanks!  
> **username_1**: 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!  

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