User defined operator in JuMP when one of the arguments is data

Specific Domains Optimization (Mathematical)
4

Your first example works because you have mixed the legacy nonlinear syntax register with the new function tracing syntax. So when you did:

julia> @objective(model, Min, norm_diff(A...))
10 A[1,1]² + 30 A[1,2]*A[1,1] + 25 A[1,2]² + 10 A[2,1]² + 30 A[2,2]*A[2,1] + 25 A[2,2]² - 2 A[1,1] - 6 A[1,2] - 6 A[2,1] - 8 A[2,2] + 2

we actually evaluated norm_diff with JuMP VariableRef as the input and got back an algebraic expression. We did not use the registered user-defined operator.

The correct syntax is:

model = Model(Ipopt.Optimizer)
@variable(model, A[1:n,1:n])
@operator(model, op_norm_diff, n^2, norm_diff)
@objective(model, Min, op_norm_diff(A...))
optimize!(model)

For your second function, it looks pretty good. But the JuMP code should be:

model = Model(Ipopt.Optimizer)
@variable(model, A[1:n,1:n])
@operator(model, op_f, n^2, f)
@objective(model, Min, op_f(A...))
optimize!(model)

This works but clearly f is type-unstable which makes its much slower than needed

Do you have evidence that the type stability makes Ipopt run slower? It probably doesn’t really matter.

I would tweak your example to be:

norm_diff_data2(A, M, I_n) = sum((A * M - I_n).^2)
g(args...) = norm_diff_data2(reshape(collect(args), n, n), M, I_n)
model = Model(Ipopt.Optimizer)
@variable(model, A[1:n,1:n])
@operator(model, op_g, n^2, g)
@objective(model, Min, op_g(A...))
optimize!(model)

but I might write it as

norm_diff_data2(A, M, I_n) = sum((A * M - I_n).^2)
model = Model(Ipopt.Optimizer)
@variable(model, A[1:n,1:n])
@objective(model, Min, norm_diff_data2(A, M, I_n))
optimize!(model)

or even

model = Model(Ipopt.Optimizer)
@variable(model, A[1:n,1:n])
@variable(model, diff[1:n,1:n])
@constraint(model, diff .== A * M .- I_n)
@objective(model, Min, sum(diff.^2))
optimize!(model)

Sorry for the delayed response. It did not allow me to edit the post at this point so my reply will contain the reproducible example.

No worries :smile: we’re not StackOverflow, so it’s even encouraged to post replies rather than editing old posts.

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