# Help optimizing a non-linear objective with JuMP
**URL:** https://discourse.julialang.org/t/help-optimizing-a-non-linear-objective-with-jump/98270
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [May 3, 2023, 6:35pm UTC](https://discourse.julialang.org/t/help-optimizing-a-non-linear-objective-with-jump/98270 "2023-05-03T18:35:27Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@mthelm85](https://discourse.julialang.org/u/mthelm85)
#### Post date: [May 3, 2023, 6:35pm UTC](https://discourse.julialang.org/t/help-optimizing-a-non-linear-objective-with-jump/98270/1 "2023-05-03T18:35:27Z")
Here is a very stripped down toy example that is roughly equivalent to my real problem (without any constraints):
```julia
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?
---
### Author:  [@abelsiqueira](https://discourse.julialang.org/u/abelsiqueira)
#### Post date: [May 3, 2023, 7:05pm UTC](https://discourse.julialang.org/t/help-optimizing-a-non-linear-objective-with-jump/98270/2 "2023-05-03T19:05:00Z")
Looks like a division by zero. Try setting a positive starting point for s.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [May 3, 2023, 9:16pm UTC](https://discourse.julialang.org/t/help-optimizing-a-non-linear-objective-with-jump/98270/3 "2023-05-03T21:16:05Z")
You should also try to add better bounds on `s`. Perhaps: `@variable(model, s[i=1:N] >= r[i])`