Question about solve time wrt dimension

[JinraeKim]

While I read the COSMO.jl paper,
I was curious about "why the solve time decreases as the dimension increases" in the case of COSMO up to n = 150:

How is it possible?

[JinraeKim]

Or, such phenomenon is it often reported from the literature?

[migarstka]

Hi @JinraeKim, thanks for noticing this. At small dimensions, where the linear system solve step dominates the computation time, I did in fact notice some variance in the solve time. The results here are from a single run of the problem set on the compute cluster. Running the same problem set multiple times and averaging the solve times should show a more congruent impact of the problem dimension on the solve time.

[JinraeKim]

Hi @JinraeKim, thanks for noticing this. At small dimensions, where the linear system solve step dominates the computation time, I did in fact notice some variance in the solve time. The results here are from a single run of the problem set on the compute cluster. Running the same problem set multiple times and averaging the solve times should show a more congruent impact of the problem dimension on the solve time.

Thank you.
Do you think it's possible from the mean values from multiple runs?
Actually, I observed this phenomenon in my case with 500 runs, so I'm inspecting the reason :)

[migarstka]

If it is systematically slower, could you send me a MWE version of the script via email or post it here? Would be interesting to see.

[JinraeKim]

@migarstka
I'm really sorry that I cannot find an appropriate MWE.
Here is my code (branch: rewrite-code); when running test/basic.jl, it gives some results with optimisation time as I said.

Sorry again that I have no idea how to find an appropriate MWE...

[JinraeKim]

Ah, it's not actually run with COSMO.jl for now, but I found that this phenomenon is also observed when solver = COSMO.