Here is a very stripped down toy example that is roughly equivalent to my real problem (without any constraints):

```
using JuMP
using Ipopt
N = 54
r = rand(N)
R = rand()
model = Model(Ipopt.Optimizer)
@variable(model, s[1:N])
@NLobjective(
model,
Min,
sum(abs((r[i]/s[i]) - R) for i in 1:N)
)
JuMP.optimize!(model)
```

`R`

is a “target ratio” and I would like to minimize the sum of the absolute differences between each of 54 different ratios and the target ratio by modifying the denominators `s`

. In my actual problem, r is a 54 x 4 matrix, there are 4 target ratios, and I have constraints that each value of `s`

can take, as well as a constraint on the sum of `s`

(and I’m trying to minimize the sum of the sums of the absolute differences). However, with the real problem and with this stripped down version, I get the following error:

Also, if I call `objective_function(model)`

it returns 0…Any ideas as to how I can formulate this problem?