Support autodiff with DifferentiationInterface

[gdalle]

Preliminary PR to run tests with the new version of NLSolversBase (which includes DI)

How should we document and test this more properly?

[blegat]

The test failures might be fixed by #1073

[gdalle]

Yeah I don't think they're related to this PR

[pkofod]

I merged 1073

[pkofod]

The test failures might be fixed by #1073

I did merge them, but I'm wondering if those fixes are related to the No nonlinear objective. errors. Could it be that the NDifferentiable are not populating all the fields they should @gdalle ?

[pkofod]

or, @blegat looking at

 exclude = String[
            # No objective
            "test_attribute_SolveTimeSec",
            "test_attribute_RawStatusString",

were more tests added that we need to exclude?

[blegat]

Yes, there might just be new tests that need to be excluded

[pkofod]

Yes, there might just be new tests that need to be excluded

one of them is this https://github.com/jump-dev/MathOptInterface.jl/blob/6bfca94b728e48a7800caf26bcc749fae86e0bc7/src/Test/test_nonlinear.jl#L1847-L1870 does that need to be excluded?

[gdalle]

Could it be that the NDifferentiable are not populating all the fields they should @gdalle ?

Looking at the NLSolversBase PR again, there is this comment that never got an answer about con_jac! being ignored, but I don't think it affects the objective.
Otherwise I can't see how we would fail to initialize some fields without errors popping up earlier in the test suite.

[gdalle]

I inserted #1133 into this PR

[pkofod]

Seems like one is saying that a nonlinear objective is not present but I cannot make out if it should be there or not. The other one is an IPNewton that fails and I'm not sure if that could be related to the constraint function you're referring to above.

[gdalle]

Do those checks also fail on main or #1133 without the new NLSolversBase, eg if we upper bound its compat to before the DI integration?

[pkofod]

Ill check later, good question !

[gdalle]

Having a baseline of failing tests is not great for adding new features 😅 if they have been failing for a while perhaps they can be marked as @test_broken

[pkofod]

Let's see what we get from #1133

[pkofod]

Also failed there. Let's try #1134

[gdalle]

Note that #1133 failed on Julia 1.6 first, where the DI-upgraded NLSolversBase cannot even be installed

[pkofod]

You can try to resolve the conflicts due to the bounds I added on master to see what happens here now

[gdalle]

@pkofod I merged master into this branch, let's see what blows up

[codecov]

Codecov Report

Attention: Patch coverage is 72.72727% with 6 lines in your changes missing coverage. Please review.

Project coverage is 86.23%. Comparing base (8e305a4) to head (f49d304).
Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/multivariate/optimize/interface.jl	72.22%	5 Missing ⚠️
...tivariate/solvers/constrained/ipnewton/ipnewton.jl	75.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1131      +/-   ##
==========================================
- Coverage   86.57%   86.23%   -0.34%     
==========================================
  Files          45       46       +1     
  Lines        3537     3531       -6     
==========================================
- Hits         3062     3045      -17     
- Misses        475      486      +11     

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[pkofod]

Okay, seems to pass. codecov complains about an unhit method, but it seems to have been like that before as well.