[petsc-users] Report Bug TaoALMM class

[Barry Smith]

  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
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> 
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> 
> <OpenPGP_0xC9BF2C20DFE9F713.asc>