[petsc-users] TAO PDIPM handling of objective evaluation failures (NaN / PDE non-convergence)

[Simon Wiesheier]

Dear PETSc developers and users,

I am considering using TAO’s Primal-Dual Interior-Point Method (PDIPM) for
a constrained optimization problem in solid mechanics. The objective
involves solving a nonlinear PDE (hyperelasticity) for each parameter
vector, and for some parameter combinations the PDE solver may fail to
converge or produce non-physical states.

With MATLAB’s fmincon, it is possible to signal such failures by returning
NaN/Inf for the objective, and the solver will then backtrack or try a
different step without crashing.

My questions are:

   1.

   How does TAO’s PDIPM handle cases where the user objective or gradient
   callback returns NaN/Inf (e.g., due to PDE solver failure)?
   2.

   Is there a recommended way in TAO/PETSc to gracefully signal an
   evaluation failure (like “bad point in parameter space”) so that the
   algorithm can back off and try a smaller step, instead of aborting?
   3.

   If the recommended pattern is *not* to return NaNs, what is the best
   practice in TAO for such PDE-constrained problems?

Any guidance on how TAO/PDIPM is intended to behave in the presence of
evaluation failures would be greatly appreciated.

Best regards,

Simon
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