How to define vector-valued @operator in JuMP

Specific Domains Optimization (Mathematical)
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4

I think you actually want to do something like this:

using JuMP
import ForwardDiff
import Ipopt

f(x) = x[1]^2 + 2*x[1]*x[2] + x[2]

function partial(f::Function, i::Int)
    function (x::Real...)
        y = collect(Real, x)
        return ForwardDiff.derivative(z -> (y[i] = z; f(y)), x[i])
    end
end

model = Model(Ipopt.Optimizer)
@variable(model, y[1:2])
rhs = @expression(model, [0.5 * y[1] * y[2], 0.2 * y[2]^2])
for i in 1:2
    name_i = Symbol("op_my_gradient_$i")
    op = add_nonlinear_operator(model, 2, partial(f, i); name = name_i)
    @constraint(model, op(y...) == rhs[i])
end
@objective(model, Max, y[1])
optimize!(model)
@assert is_solved_and_feasible(model)
value.(y)
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