[petsc-users] Tao TRON solver tolerances

[Justin Chang]

Hi again,

I was reading through the TAO manual and the impression I am getting is
that the KSP solver computes the gradient/projection, not necessarily the
solution itself. Meaning it matters not how accurate this projection is, so
long as the actual objective tolerance is met.

Is this a correct assessment of why one can get away with a less stringent
KSP tolerance and still attain an accurate solution?

Thanks,
Justin

On Tuesday, March 8, 2016, Justin Chang <jychang48 at gmail.com
<javascript:_e(%7B%7D,'cvml','jychang48 at gmail.com');>> wrote:

> Hi all,
>
> So I am solving a convex optimization problem of the following form:
>
> min 1/2 x^T*H*x - x^T*f
> s.t. 0 < x < 1
>
> Using the TAOTRON solver, I also have CG/ILU for KSP/PC. The following TAO
> solver tolerances are used for my specific problem:
>
> -tao_gatol 1e-12
> -tao_grtol 1e-7
>
> I noticed that the KSP tolerance truly defines the performance of this
> solver. Attached are three run cases with -ksp_rtol 1e-7, 1e-3, and 1e-1
> with "-ksp_converged_reason -ksp_monitor_true_residual -tao_view
> -tao_converged_reason -log_view". It seems that the lower the KSP
> tolerance, the faster the time-to-solution where the number of KSP/TAO
> solve iterations remains roughly the same.
>
> So my question is, is this "normal"? That is, if using TRON, one may relax
> the KSP tolerances because the convergence of the solver is primarily due
> to the objective functional from TRON and not necessarily the KSP solve
> itself? Is there a general rule of thumb for this, because it would seem to
> me that for any TRON solve I do, i could just set a really low KSP rtol and
> still get roughly the same performance.
>
> Thanks,
> Justin
>
>
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