Is there a way I could do this? I understand that JuMP has some restrictions that may present a challenge but I’m open to any reasonable implementations!

There is also a hack for user-defined functions which return a vector:

Longer-term, we’re in the middle of a rewrite to JuMP’s nonlinear interface, https://github.com/jump-dev/JuMP.jl/pull/3106, which will make this work with no hacks or registered functions.

(p.s. I was having a conversation with @ccoffrin a few hours ago that this is the most common question I get about JuMP. It comes up a few times every week… So hopefully we’ll have a better answer once that PR is merged.)

I ended up doing a very hackish implementation using Symbolics

using JuMP
using Ipopt
import Symbolics
@Symbolics.variables x[1:2]
x = Symbolics.scalarize(x)
function g(x)
[
x[1]^4 + x[2]^5,
exp(x[1])
]
end
function o(x)
exp(x[1]) + exp(x[2])
end
C = g(x)
O = o(x)
m = Model(Ipopt.Optimizer)
# replace variable
@variable(m, x[1:2])
for i in eachindex(C)
eval("@NLconstraint(m, $(repr(C[i])) <= 0")
end
eval("@NLobjective(m, Min, $(repr(O)))")
optimize!(m)
println(value.(x))

The use of eval isn’t very safe, and you’ll likely run into a bunch of scoping issues. A better approach is to use the raw expression input: Nonlinear Modeling · JuMP

using JuMP
import Symbolics
to_expression(f, x::Vector{VariableRef}) = f
function to_expression(f::Expr, x::Vector{VariableRef})
if Meta.isexpr(f, :ref)
return x[f.args[2]]
end
for i in 1:length(f.args)
f.args[i] = to_expression(f.args[i], x)
end
return f
end
function to_expression(f::Function, x::Vector{VariableRef})
Symbolics.@variables(y[1:length(x)])
f_y = f(Symbolics.scalarize(y))
if f_y isa Vector
return [to_expression(Meta.parse("$f_i"), x) for f_i in f_y]
else
return to_expression(Meta.parse("$f_y"), x)
end
end
g(x) = [x[1]^4 + x[2]^5, exp(x[1])]
o(x) = exp(x[1]) + exp(x[2])
model = Model()
@variable(model, x[1:2])
set_nonlinear_objective(model, MOI.MIN_SENSE, to_expression(o, x))
for gi in to_expression(g, x)
add_nonlinear_constraint(model, :($gi <= 0))
end
print(model)