>
> The function tolerances are usually something like |f(x_k) - f_(x_{k-1})|
> <= fatolBut that is *not* what they are in TAO, this has always been a source of confusion. The one upside of the f-tolerances is that they give the users a reasonable level of confidence that the objective function value achieved is within ftol of the true minimum, but it just happens to be redundant because f(x)-f(X*) is estimated using ||g(x)||^2 (How? I thought this made sense to me once, but now I don't see it anymore) and we also have a convergence criteria for ||g(x)||. On Wed, Sep 9, 2015 at 10:02 AM, Munson, Todd S. <[email protected]> wrote: > > I do not see a need to keep them around. The function tolerances are > usually something like |f(x_k) - f_(x_{k-1})| <= fatol and then you > use |f(x_0)| in the denominator for the relative tolerance. There > are pretty useless tests though and give many false positives. > > Todd. > > > On Sep 9, 2015, at 9:26 AM, Jason Sarich <[email protected]> wrote: > > > > Todd, can you come up with a reason why we might need to keep these > fatol, frtol tests around? I would prefer to take them out. > > > > Jason > > > > On Tue, Sep 8, 2015 at 9:54 PM, Smith, Barry F. <[email protected]> > wrote: > > > > Jason, > > > > Perhaps it is just documentation. > > > > /*@ > > TaoSetTolerances - Sets parameters used in TAO convergence tests > > > > Logically collective on Tao > > > > Input Parameters: > > + tao - the Tao context > > . fatol - absolute convergence tolerance > > . frtol - relative convergence tolerance > > . gatol - stop if norm of gradient is less than this > > . grtol - stop if relative norm of gradient is less than this > > - gttol - stop if norm of gradient is reduced by this factor > > > > Options Database Keys: > > + -tao_fatol <fatol> - Sets fatol > > . -tao_frtol <frtol> - Sets frtol > > . -tao_gatol <gatol> - Sets gatol > > . -tao_grtol <grtol> - Sets grtol > > - -tao_gttol <gttol> - Sets gttol > > > > Stopping Criteria: > > $ f(X) - f(X*) (estimated) <= fatol > > $ |f(X) - f(X*)| (estimated) / |f(X)| <= frtol > > $ ||g(X)|| <= gatol > > $ ||g(X)|| / |f(X)| <= grtol > > $ ||g(X)|| / ||g(X0)|| <= gttol > > > > How is f(x) - f(X*) (estimated) and how come the second definition has > absolute values but the first does not? > > > > From below it looks like f(x) - f(X*) is estimated as gnorm*gnorm? > > > > } else if (gnorm2 <= fatol && cnorm <=catol) { > > ierr = PetscInfo2(tao,"Converged due to estimated f(X) - f(X*) = %g > < %g\n",(double)gnorm2,(double)fatol);CHKERRQ(ierr); > > reason = TAO_CONVERGED_FATOL; > > } else if (f != 0 && gnorm2 / PetscAbsReal(f)<= frtol && > cnorm/PetscMax(cnorm0,1.0) <= crtol) { > > ierr = PetscInfo2(tao,"Converged due to estimated |f(X)-f(X*)|/f(X) > = %g < %g\n",(double)(gnorm2/PetscAbsReal(f)),(double)frtol);CHKERRQ(ierr); > > reason = TAO_CONVERGED_FRTOL; > > > > It seems the next test is the same as the first I list above exact gnorm > is not squared? Why is it worth having this duplicate test? > > > > } else if (gnorm<= gatol && cnorm <=catol) { > > ierr = PetscInfo2(tao,"Converged due to residual norm ||g(X)||=%g < > %g\n",(double)gnorm,(double)gatol);CHKERRQ(ierr); > > reason = TAO_CONVERGED_GATOL; > > > > At a minimum the manual page should document what f(X) - f(X*) > (estimated) means. > > > > Barry > > > > } else if ( f!=0 && PetscAbsReal(gnorm/f) <= grtol && cnorm <= crtol) { > > ierr = PetscInfo2(tao,"Converged due to residual ||g(X)||/|f(X)| =%g > < %g\n",(double)(gnorm/f),(double)grtol);CHKERRQ(ierr); > > > > > >
