add relative tolerance to BranchAndBoundEnclosure

[aplavin]

Thanks for the package, it's already very useful and convenient!

Here, I suggest to add an rtol argument, so that one can easily specify the target tolerance independent on the scale of values in a problem.

If this addition is welcome, we can discuss the best way to backwards compatibility: either keep tol and not rename it to atol, or add a tol alias for atol.

[schillic]

Thanks for the proposal. I do not fully understand. Can you give an example?

[aplavin]

Basically, this PR makes it possible to run enclose for functions with very different scales (think f(x) and 1e10 * f(x)) with the same options: just specify rtol!

Currently, tol is absolute, and tol = 1e-3 is a very big tolerance for f(x) = 1e-10 * x (will stop on the first iteration), but is a very small tolerance for f(x) = 1e10 * x (will only stop at maxdepth).

[schillic]

Okay, makes sense now. Some comments:

• We need to make a breaking release in any case because the behavior will change. I do not mind that at all.
• The old behavior is atol=1e-3, and now atol=1e-6. I do not have an opinion which one to choose.
• I prefer to be clear, i.e., to rename the field to atol. We could offer a constructor with a tol alias for atol, as you suggest, but I do not think this is necessary. Getting a crash is better than a silent change of behavior IMO.
• Before merging, a couple of changes are required:
  • The docstring should be updated
  • The failing tests should be adapted to the new interface.
  • There should be new tests demonstrating that the new version works as intended (could be the examples you gave).

@mforets, @lucaferranti, what do you think?

[lucaferranti]

This is the definition of mignitude

Suggested change

	min_abs = in_interval(0, fX) ? zero(fX.lo) : min(abs(fX.lo), abs(fX.hi))
	min_abs = mig(fX)

[schillic]

Nice. Then I suggest to inline the function instead of having this extra line.

[lucaferranti]

I dont think we need an alias, let's just rename tol to atol and make a breaking change. The new naming conention is also closer to that of other functions in the julia ecosystem