<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div><br></div> Thanks for your response and the code. I understand the potential problem and how your code demonstrates a bug if the TaoALMMSubsolverObjective() is used in the manner you use in the example where you directly call TaoComputeObjective() multiple times line a line search code might.<div><br></div><div> What I don't have or understand is how to reproduce the problem in a real code that uses Tao. That is where the Tao <span style="font-family: monospace;">Armijo</span> line search code has a problem when it is used (somehow) in a Tao solver with ALMM. You suggest "<span style="font-family: monospace;">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." I don't see how to do this if I use -tao_type </span><font face="monospace">almm I cannot use </font><span style="font-family: monospace;">-tao_ls_type armijo; that is the option </span><span style="font-family: monospace;">-tao_ls_type doesn't seem to me to be usable in the context of almm (since almm internally does directly its own trust region approach for globalization). If we remove the if (1) code from your example, is there some Tao options I can use to get the bug to appear inside the Tao solve?</span></div><div><span style="font-family: monospace;"><br></span></div><div><font face="monospace">I'll try to explain again, I agree that the fact that the Tao solution is aliased (within the ALMM solver) is a problem with repeated calls to </font>TaoComputeObjective() but I cannot see how these repeated calls could ever happen in the use of TaoSolve() with the ALMM solver. That is when is this "design problem" a true problem as opposed to just a potential problem that can be demonstrated in artificial code?</div><div><br></div><div>The reason I need to understand the non-artificial situation it breaks things is to come up with an appropriate correction for the current code.</div><div><br></div><div> Barry</div><div><br></div><div><br></div><div><span style="font-family: monospace;"><br></span></div><div><span style="font-family: monospace;"><br></span></div><div><br></div><div><br></div><div><div><br><blockquote type="cite"><div>On Nov 3, 2022, at 12:46 PM, Stephan Köhler <stephan.koehler@math.tu-freiberg.de> wrote:</div><br class="Apple-interchange-newline"><div>
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<font face="monospace">Barry,<br>
<br>
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. <br>
<br>
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. <br>
It is also possible that, by luck, it will cause no problems, if
the </font><font face="monospace"><var title="adjective">"excessive"</var>
step brings a reduction of the objective<br>
<br>
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.<br>
The import part begins at line 292 in test_tao_neohooke.cpp<br>
<br>
Stephan<br>
</font><br>
<div class="moz-cite-prefix">On 02.11.22 19:04, Barry Smith wrote:<br>
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<blockquote type="cite" cite="mid:AB01B851-54B1-4878-B08D-0D15CB3EA825@petsc.dev">
<pre class="moz-quote-pre" wrap=""> 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
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<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">On Oct 28, 2022, at 4:27 AM, Stephan Köhler <a class="moz-txt-link-rfc2396E" href="mailto:stephan.koehler@math.tu-freiberg.de"><stephan.koehler@math.tu-freiberg.de></a> 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., <a class="moz-txt-link-freetext" href="https://petsc.org/release/src/tao/constrained/impls/almm/almm.c.html">https://petsc.org/release/src/tao/constrained/impls/almm/almm.c.html</a> 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., <a class="moz-txt-link-freetext" href="https://petsc.org/release/src/tao/linesearch/impls/armijo/armijo.c.html">https://petsc.org/release/src/tao/linesearch/impls/armijo/armijo.c.html</a> 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>
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<pre class="moz-signature" cols="72">--
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)</pre>
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