# Nonlinear optimization in JuMP adding the analytic gradient expression
**URL:** https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [March 31, 2023, 12:26am UTC](https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867 "2023-03-31T00:26:38Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@mb96](https://discourse.julialang.org/u/mb96)
#### Post date: [March 31, 2023, 12:26am UTC](https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867/1 "2023-03-31T00:26:38Z")
Hi, I am trying to solve a highly dimensional nonlinear optimization problem for which I have a function that maps a vector into a value and a its jacobian. I want to solve the problem providing the gradient but I can not find good resources that explain how to do so using the Optim package. Can anyone point to resources or provide a very simple example illustrating how to set up the problem?
Thanks in advance,
Miguel.
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### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [March 31, 2023, 1:51am UTC](https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867/2 "2023-03-31T01:51:41Z")
Do you have only a single function to optimize? Are there other constraints? Integrality or bounds on the variables?
You can register a user-defined function in JuMP and provide the analytic gradient: [Nonlinear Modeling · JuMP](https://jump.dev/JuMP.jl/stable/manual/nlp/#Multivariate-functions)
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### Author:  [@mb96](https://discourse.julialang.org/u/mb96)
#### Post date: [March 31, 2023, 2:58pm UTC](https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867/3 "2023-03-31T14:58:17Z")
Thanks!
I am trying to adapt the example in the documentation so that it takes in a vector instead its elements explicitly because in my problem I am solving a 15 dimensional problem. However, when I do this it assumes it is univariate function. I illustrate this below:
When I call the function I run into this error:
Any ideas on how to fix this?
Thanks a lot!
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### Author:  [@Adedayo\_Yusuff](https://discourse.julialang.org/u/Adedayo_Yusuff)
#### Post date: [April 9, 2023, 4:15am UTC](https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867/4 "2023-04-09T04:15:54Z")
I think you should use splat f(x…).
There is an example on this in [Nonlinear Modeling · JuMP](https://jump.dev/JuMP.jl/stable/manual/nlp/#Multivariate-functions).
```julia
f(x...) = (1 - x[1])^2 + 100 * (x[2] - x[1]^2)^2
function ∇f(g, x...)
g[1] = 400 * x[1]^3 - 400 * x[1] * x[2] + 2 * x[1] - 2
g[2] = 200 * (x[2] - x[1]^2)
return
end
function ∇²f(H, x...)
H[1, 1] = 1200 * x[1]^2 - 400 * x[2] + 2
# H[1, 2] = -400 * x[1] <-- Not needed. Fill the lower-triangular only.
H[2, 1] = -400 * x[1]
H[2, 2] = 200.0
return
end
model = Model()
register(model, :rosenbrock, 2, f, ∇f, ∇²f)
@variable(model, x[1:2])
@NLobjective(model, Min, rosenbrock(x[1], x[2]))
```
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### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [April 9, 2023, 8:50pm UTC](https://discourse.julialang.org/t/nonlinear-optimization-in-jump-adding-the-analytic-gradient-expression/96867/5 "2023-04-09T20:50:04Z")
Ooops. I never replied to this.
@Adedayo_Yusuff is correct. You need to use the splatted syntax. You cannot pass a `Vector` as a single argument.