Implement empty! and is_empty for MOI.Nonlinear.Model

[blegat]

Would be useful for JuliaManifolds/Manopt.jl#264

[odow]

Just build a new one? MOI.Nonlinear.Model does not follow the full MOI API.

[blegat]

Indeed, it's a bit confusing it does not

[odow]

Not really, it doesn't add variables via add_variable, it doesn't manage the objective via set(m, ::ObjectiveFunction) because the function type is Expr, and so on. It's not a heavy lift to have to create a new one rather than call empty!.

[blegat]

Ok but I guess is_empty would still be useful, I was wondering why Ipopt was not checking the nlp_model fields in its MOI.is_empty

[odow]

You don't really need this for ManOpt: https://github.com/JuliaManifolds/Manopt.jl/pull/264/files#r1348482364

And I guess for ipopt we could check if nlp_model === nothing, but it's not really important.
https://github.com/jump-dev/Ipopt.jl/blob/e01818b6bde26ef779df08be9108694e75613b41/src/MOI_wrapper.jl#L105C5-L105C20