# Setting nonlinear objectives with JuMP
**URL:** https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [April 11, 2022, 12:29pm UTC](https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343 "2022-04-11T12:29:29Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Hans\_W\_Borchers](https://discourse.julialang.org/u/Hans_W_Borchers)
#### Post date: [April 11, 2022, 12:29pm UTC](https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343/1 "2022-04-11T12:29:29Z")
Dear All, one year ago I have written a small note on how to use Julia from R through the ‘JuliaCall’ package. I wanted to update this page and encountered some problems with Julia’s JuMP package.
See Notes on JuliaCall at [https://hwborchers.github.io/](https://hwborchers.github.io/).
The problem I wanted to solve is minimizing the (generalized) Rosenbrock funtion with constraints `0.0 <= x_i` and `sum(x)==1`. Rosenbrock is defined as
```julia
function rosen(x...)
n = length(x); s = 0.0
for i = 1:length(x)-1
s += 100*(x[i+1] - x[i]^2)^2 + (x[i] - 1)^2
end
return s
end
```
Here is the version for minimizing Rosenbrock (with constraints `0.0<=x_i<=0.5` only) that was correct last year:
```julia
01 using JuMP, Ipopt
02 m = Model(solver = IpoptSolver());
03 @variable(m, 0.0 <= x[1:10] <= 0.5);
04 for i in 1:10 setvalue(x[i], 0.1); end;
05 JuMP.register(m, :rosen, 10, rosen, autodiff=true);
06 JuMP.setNLobjective(m, :Min,
07 Expr(:call, :rosen, [x[i] for i=1:10]...));
08 sol = solve(m);
09 getvalue(x)
## [1] 0.5000000000 0.2630659929 0.0800311191 0.0165742352 0.0103806763
## [6] 0.0102120052 0.0102084109 0.0102042121 0.0100040851 0.0001000822
```
Please note that lines (5-7) have been suggested to me when I asked for help here on the Julia discussion forum.
I have learned by now that I have to make the following changes:
(2) Replace the solver in the Model call with “Model(Ipopt.Optimizer)”
(8) Replace “solve” with “optimize!”
(9) Replace “getvalue(x)” with “JuMP.value.(x)”
It is still unclear to me, and I tried to find something in the documentation:
(5) Do I still need to register the rosen function?
(\*) Do I need to set the @NLexpression ?
(6) How to set a nonlinear objective function (with setNLobjective)?
If I can get this example right, I think I can do the rest of my applications alone. Of course, a link to proper documentation pages will also be helpful.
Many thanks.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [April 11, 2022, 5:37pm UTC](https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343/2 "2022-04-11T17:37:40Z")
Is this sufficient?
```julia
using JuMP
import Ipopt
m = Model(Ipopt.Optimizer)
@variable(m, 0.0 <= x[1:10] <= 0.5, start = 0.1)
register(m, :rosen, 10, rosen, autodiff=true)
@NLobjective(m, Min, rosen(x...))
optimize!(m)
value(x)
```
If you want to see the raw expression input, here are the docs; [Nonlinear Modeling · JuMP](https://jump.dev/JuMP.jl/stable/manual/nlp/#Raw-expression-input)
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [April 11, 2022, 7:22pm UTC](https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343/3 "2022-04-11T19:22:14Z")
I’ll also add, the old code you reference is from JuMP v0.18. We changed a lot during the transition to MathOptInterface in 2019. But we recently released JuMP 1.0, [JuMP 1.0.0 is released | JuMP](https://jump.dev/blog/1.0.0-release/), so this is the syntax you can rely on without the risk of things breaking in future.
---
### Author:  [@Hans\_W\_Borchers](https://discourse.julialang.org/u/Hans_W_Borchers)
#### Post date: [April 11, 2022, 7:46pm UTC](https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343/4 "2022-04-11T19:46:25Z")
Thanks a lot. In the meantime, I managed to get this to work. I still think there should be some more examples concerning nonlinear objective functions and constraints. On the other hand: As I got this to run before I read your answer, the docs are not bad 🙂 !
```julia
function rosen(x...)
n = length(x); s = 0.0
for i = 1:length(x)-1
s += 100*(x[i+1] - x[i]^2)^2 + (x[i] - 1)^2
end
return s
end
using JuMP, Ipopt
m = Model(Ipopt.Optimizer);
@variable(m, 0.0 <= x[1:10] <= 1.0);
for i in 1:10 setvalue(x[i], 0.1); end;
@constraint(m, c1, sum(x) == 1.0);
JuMP.register(m, :rosen, 10, rosen, autodiff=true);
@NLexpression(m, e1, rosen(x...));
@NLobjective(m, Min, e1);
sol = optimize!(m);
xmin = JuMP.value.(x)
## 10-element Vector{Float64}:
## 0.5
## 0.2759742637043274
## 0.09633073776545037
## 0.027604360420402374
## 0.018857245635309217
## 0.018439883710793973
## 0.018423364058042388
## 0.018408615621349985
## 0.01803449829941936
## 0.007927020786201111
rosen(xmin...)
## 7.663371563695662
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [April 11, 2022, 7:59pm UTC](https://discourse.julialang.org/t/setting-nonlinear-objectives-with-jump/79343/5 "2022-04-11T19:59:18Z")
Is this section sufficient? [Introduction · JuMP](https://jump.dev/JuMP.jl/stable/tutorials/nonlinear/introduction/)