Josua Grawitter

It looks like you are following this Tutorial — is that correct? https://julianlsolvers.github.io/Optim.jl/stable/#examples/generated/ipnewton_basics/#generic-nonlinear-constraints

I suspect the following: IPNewton allocates some memory without zero-ing it. (eg here https://github.com/JuliaNLSolvers/Optim.jl/blob/cdebfcacb58ad52256342d8e8e8754b1bb92dcde/src/multivariate/solvers/constrained/ipnewton/ipnewton.jl#L111 )That memory can contain `NaN`, infinities, etc. Depending on the way you define your methods `con_c!`,...

After looking into it more deeply: These allocations all happen in `initial_state()` which means they only happen once. I think it will not affect performance too much to replace them...

I have no objection to removing the `signbit` method from IntervalArithmetic. Since NumberIntervals imports it from Base and implements its own method, I doubt I even need to adapt anything.

> > > QR makes sense in that its the QR decomposition calculated via interval arithmetic. That is, Q and R are intervals containing the true QR decomposition. > >...

I'm certainly not claiming that it's impossible to invert/decompose a matrix - the problem is that IntervalArithmetic.jl has no way of telling users *when* it's impossible (again, see the issue...

> > > Like I said: don’t let the perfect be enemy of the good. I encountered this issue because I needed it. I guess that is kind of my...

> > > I'm not sure what you mean by "cannot be solved" here. As we saw in https://github.com/JuliaArrays/StaticArrays.jl/issues/450 sometimes external algorithms give somewhat unpredictable results when confronted with IntervalArithmetic.jl's...

> > > I actually quite like the solution in `NumberIntervals`. It's a clever way of introducing a 3-valued logic by returning `missing` when both `true` and `false` are correct...

> @gwater How does the 3-valued logic affect performance though? Since that introduces a weak type instability, right? I haven't benchmarked it yet but from what I hear these small...