MAINT: Skip the check for theta <= 1 in the PDHG

[sbanert]

DOC: Update the PDHG docstring to latest research.

The Chambolle-Pock method converges even for $\theta &gt; 1$, so the check that requires the contrary (and aborts with an error otherwise) should be removed. I also updated the docstring with a paper of ours that shows relaxed requirements on the step lengths.

Moreover, I removed certain statements that seem unnecessary from the docstring like the requirement that the spaces be finite-dimensional (for infinite-dimensional spaces, the convergence is weak, as is standard for these methods), and that the functionals be non-negative (this is definitely not needed).

I am not even sure if it is good to keep the check for non-negativity of $\theta$ in the code. If users try to experiment with negative $\theta$, why not? Our code should not break in this case. The check for $\theta \leq 1$ currently prevents us from using this method for numerical experiments for the paper [BUG2023].

[pep8speaks]

Checking updated PR...

No PEP8 issues.

Comment last updated at 2024-02-13 18:45:18 UTC

[ozanoktem]

Agree that the solver should in general not prevent a user to call it with parameter settings that does not guarantee convergence. Perhaps it is enough that the solver raises a warning when it is used in this way.