Dave,
You could explore adding the "hook step" feature to the current TR code.
We've never done it due to lack of resources and low priority for us but it is
a completely reasonable thing to support.
Barry
> On May 9, 2019, at 10:41 PM, Dave Lee <davelee2...@gmail.com> wrote:
>
> Thanks Barry,
>
> I will try reducing the default -snes_tr_delta0 from 0.2 to 0.1, and also
> take a look at using the line search method as well.
>
> The reason I wanted to use the trust region solver instead is that previous
> studies of my problem have used the "hook step" method, which I gather is
> more in line with the trust region method in that it first chooses a step
> size and then determines a direction for which convergence is ensured w.r.t.
> the step size, and not vice versa, as I gather is the case for the line
> search algorithm.
>
> Thanks again, Dave.
>
>
>
> On Fri, May 10, 2019 at 3:56 AM Smith, Barry F. <bsm...@mcs.anl.gov> wrote:
>
>
> > On May 9, 2019, at 3:39 AM, Dave Lee via petsc-users
> > <petsc-users@mcs.anl.gov> wrote:
> >
> > Hi PETSc,
> >
> > I'm using the SNES trust region to solve a matrix free Newton problem. I
> > can't see a lot of description of the trust region algorithm in the manual
> > (section 5.2.2), and have also found it difficult to find documentation on
> > the MINPACK project from which it is apparently derived. I have a couple of
> > questions about this:
> >
> > 1) Is the PETSc SNES trust region algorithm the same as the "hook step"
> > algorithm detailed in Section 6.4.1 of Dennis and Schnabel (1996)
> > "Numerical methods for Unconstrained Optimization and Nonlinear Equations"?
>
> No. It is more naive than that. If the trust region is detected to be too
> big it does a simple backtracking until it gets a sufficient decrease in the
> function norm. The "true" trust region algorithms do something more clever
> than just back tracking along the Newton direction.
>
> >
> > 2) Is there anywhere I can find specific documentation on the trust region
> > control parameters as defined in:
> > https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNESNEWTONTR.html#SNESNEWTONTR
>
> You need to look at the code. It is in src/snes/impls/tr/tr.c It is very
> simple.
>
>
> >
> > 3) My solve returns before it is sufficiently converged.
>
> Define sufficiently converged? The whole point of trust regions is that
> the nonlinear solver/optimization algorithm decides when to stop the linear
> solver, not your measure of the residual of the linear system.
>
> > On the last few Newton iterations the KSP converges due to:
> > CONVERGED_STEP_LENGTH
> > after only a couple of KSP iterations. What is the default for this
> > parameter?, and how can I change it? Should I change it?
>
> The name is slightly confusing. This means the solver has reached the size
> of the trust region. To change this value means to change the size of the
> trust region. The initial size of the trust region is given by
> delta0*norm2(x) (or delta0 if x == 0). See SNESNEWTONTR. You can control
> delta0 with -snes_tr_delta0 delta0. After you start the algorithm it
> automatically adjusts the size of the trust region making it bigger or
> smaller based on how well Newton is working.
>
> Normally as Newton's method starts to converge well the trust region gets
> bigger and bigger (and hence the linear solver is solved more and more
> accurately). If the trust region doesn't grow it usually means something has
> gone wrong.
>
> Note you can run with -info to see with more detail what decisions the
> trust region algorithm is making..
>
> I'm not sure I recommend you spend a lot of time on the trust region
> approach. The various line searches in PETSc are more robust and mature and
> if they fail you the trust region code is unlikely to save you.
>
> Barry
>
>
>
> >
> > Cheers, Dave.
>
