[petsc-users] Report Bug TaoALMM class

[Stephan Köhler]

Barry,

so far, I have not experimented with trust-region methods, but I can 
imagine that this "design feature" causes no problem for trust-region 
methods, if the old point is saved and after the trust-region check 
fails the old point is copied to the actual point.  But the 
implementation of the Armijo line search method does not work that way.  
Here, the actual point will always be overwritten.  Only if the line 
search fails, then the old point is restored, but then the TaoSolve 
method ends with a line search failure.

If you have an example for your own, you can switch the Armijo line 
search by the option -tao_ls_type armijo.  The thing is that it will 
cause no problems if the line search accepts the steps with step length 
one.
It is also possible that, by luck, it will cause no problems, if the 
"excessive" step brings a reduction of the objective

Otherwise, I attach my example, which is not minimal, but here you can 
see that it causes problems.  You need to set the paths to the PETSc 
library in the makefile.  You find the options for this problem in the 
run_test_tao_neohooke.sh script.
The import part begins at line 292 in test_tao_neohooke.cpp

Stephan

On 02.11.22 19:04, Barry Smith wrote:
>    Stephan,
>
>      I have located the troublesome line in TaoSetUp_ALMM() it has the line
>
>    auglag->Px = tao->solution;
>
> and in alma.h it has
>
> Vec  Px, LgradX, Ce, Ci, G;         /* aliased vectors (do not destroy!) */
>
> Now auglag->P in some situations alias auglag->P  and in some cases auglag->Px serves to hold a portion of auglag->P. So then in TaoALMMSubsolverObjective_Private()
> the lines
>
> PetscCall(VecCopy(P, auglag->P));
>   PetscCall((*auglag->sub_obj)(auglag->parent));
>
> causes, just as you said, tao->solution to be overwritten by the P at which the objective function is being computed. In other words, the solution of the outer Tao is aliased with the solution of the inner Tao, by design.
>
> You are definitely correct, the use of TaoALMMSubsolverObjective_Private and TaoALMMSubsolverObjectiveAndGradient_Private  in a line search would be problematic.
>
> I am not an expert at these methods or their implementations. Could you point to an actual use case within Tao that triggers the problem. Is there a set of command line options or code calls to Tao that fail due to this "design feature". Within the standard use of ALMM I do not see how the objective function would be used within a line search. The TaoSolve_ALMM() code is self-correcting in that if a trust region check fails it automatically rolls back the solution.
>
>    Barry
>
>
>
>
>> On Oct 28, 2022, at 4:27 AM, Stephan Köhler<stephan.koehler at math.tu-freiberg.de>  wrote:
>>
>> Dear PETSc/Tao team,
>>
>> it seems to be that there is a bug in the TaoALMM class:
>>
>> In the methods TaoALMMSubsolverObjective_Private and TaoALMMSubsolverObjectiveAndGradient_Private the vector where the function value for the augmented Lagrangian is evaluate
>> is copied into the current solution, see, e.g.,https://petsc.org/release/src/tao/constrained/impls/almm/almm.c.html  line 672 or 682.  This causes subsolver routine to not converge if the line search for the subsolver rejects the step length 1. for some
>> update.  In detail:
>>
>> Suppose the current iterate is xk and the current update is dxk. The line search evaluates the augmented Lagrangian now at (xk + dxk).  This causes that the value (xk + dxk) is copied in the current solution.  If the point (xk + dxk) is rejected, the line search should
>> try the point (xk + alpha * dxk), where alpha < 1.  But due to the copying, what happens is that the point ((xk + dxk) + alpha * dxk) is evaluated, see, e.g.,https://petsc.org/release/src/tao/linesearch/impls/armijo/armijo.c.html  line 191.
>>
>> Best regards
>> Stephan Köhler
>>
>> -- 
>> Stephan Köhler
>> TU Bergakademie Freiberg
>> Institut für numerische Mathematik und Optimierung
>>
>> Akademiestraße 6
>> 09599 Freiberg
>> Gebäudeteil Mittelbau, Zimmer 2.07
>>
>> Telefon: +49 (0)3731 39-3173 (Büro)
>>
>> <OpenPGP_0xC9BF2C20DFE9F713.asc>

-- 
Stephan Köhler
TU Bergakademie Freiberg
Institut für numerische Mathematik und Optimierung

Akademiestraße 6
09599 Freiberg
Gebäudeteil Mittelbau, Zimmer 2.07

Telefon: +49 (0)3731 39-3173 (Büro)

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