# ERROR: The objective function (erf) is not supported by JuMP
**URL:** https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [October 13, 2020, 2:19pm UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302 "2020-10-13T14:19:28Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@BuRanran](https://discourse.julialang.org/u/BuRanran)
#### Post date: [October 13, 2020, 2:19pm UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/1 "2020-10-13T14:19:28Z")
I have a non-linear optimization problem to be solved with JuMP and IPOPT solver. The objective function is a probability distribution function of a normal distribution. It can be optimized by IPOPT directly, but not supported by JuMP. Is there any method to solve this problem? As the constrains are complicated, I hope to write constrains with JuMP. Thanks a lot !
The codes with error are as follows.
```julia
func1(x)=1/(2*3.1415926)^0.5/20*exp(-(x-100)^2/2/20^2)
gp = Model(with_optimizer(Ipopt.Optimizer))
@variable(gp, Q)
@objective(gp, Max, integrate(func1)(Q))
optimize!(gp)
```
ERROR: LoadError: The objective function `0.199471141902022*sqrt(2)*sqrt(pi)*erf(sqrt(2)*(x - 100)/40)` is not supported by JuMP.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 13, 2020, 9:59pm UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/2 "2020-10-13T21:59:10Z")
Here are the docs: [https://jump.dev/JuMP.jl/stable/nlp/](https://jump.dev/JuMP.jl/stable/nlp/)
You need to use `@NLobjective` and `@NLconstraint`.
You will also need to register the `integrate` function as a user-defined function, so something like:
```nohighlight
using JuMP
using Ipopt
gp = Model(Ipopt.Optimizer)
@variable(gp, Q)
func1 = integrate(1/(2*3.1415926)^0.5/20*exp(-(x-100)^2/2/20^2))
register(gp, :func1, 1, func1; autodiff=true)
@NLobjective(gp, Max, func1(Q))
optimize!(gp)
```
Note that I haven’t tested this because I don’t know where `integrate` comes from.
---
### Author:  [@BuRanran](https://discourse.julialang.org/u/BuRanran)
#### Post date: [October 14, 2020, 2:43am UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/3 "2020-10-14T02:43:34Z")
Thanks for your reply. I correct the @objective to @NLobjective, it really helps. But there are still errors.
Ps. The `integrate()` is a integral function in package “SymPy”
```julia
using JuMP
using Ipopt
using SymPy
gp = Model(Ipopt.Optimizer)
@variable(gp, Q)
func1(x)=1/(2*3.1415926)^0.5/20*exp(-(x-100)^2/2/20^2)
func2(y)=integrate(func1, -Inf, y)
register(gp, :func2, 1, func2; autodiff=true)
@NLobjective(gp, Max, func2(Q))
optimize!(gp)
```
ERROR: LoadError: Expected return type of Float64 from a user-defined function, but got Sym.
That the type of `func2(constant)` is `Sym`, for example:
```julia
julia> func2(100)
0.199471141902022⋅√2⋅√π
julia> typeof(func2(100))
Sym
```
I want to transfer `Sym` to `float` by using function `float(func2(Q))`, but function `float()` can not be used in the objective. How can I fix this problem?
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 14, 2020, 5:32am UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/5 "2020-10-14T05:32:49Z")
You want something like
```nohighlight
using JuMP
using Ipopt
using SymPy
func1(x)=1/(2*3.1415926)^0.5/20*exp(-(x-100)^2/2/20^2)
func2 = lambdify(integrate(func1))
func3(y) = convert(Real, func2(y))
gp = Model(Ipopt.Optimizer)
@variable(gp, Q)
register(gp, :func3, 1, func3; autodiff=true)
@NLobjective(gp, Max, func3(Q))
optimize!(gp)
```
---
### Author:  [@BuRanran](https://discourse.julialang.org/u/BuRanran)
#### Post date: [October 15, 2020, 7:01am UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/6 "2020-10-15T07:01:45Z")
It works. Thanks so much!
---
### Author:  [@anand.kumar](https://discourse.julialang.org/u/anand.kumar)
#### Post date: [August 13, 2024, 12:45pm UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/7 "2024-08-13T12:45:39Z")
Have something similar and was trying to replicate this. However, it seems syntax has updated for SymPy. Got it working, but `convert` doesn’t seem to work.
update: realised func(z) returns float64. Thus, I may not need convert (maybe?). However, adding this in objective function yields back `erf` in the expression and I’m back to square -
In my case, objective function involves `f(u,w) + g(u)*erf(u/w)`. Since, `erf` isn’t defined in Julia natively, I’m hoping, resorting to your approach could work for my case too. I’m using standard solver e.g. Gurobi/Knitro. Any other insights would be helpful.
Thank You.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [August 13, 2024, 10:17pm UTC](https://discourse.julialang.org/t/error-the-objective-function-erf-is-not-supported-by-jump/48302/8 "2024-08-13T22:17:46Z")
Hi @anand.kumar,
`erf` is supported as part of SpecialFunctions.jl
See the JuMP documentation section: [Nonlinear Modeling · JuMP](https://jump.dev/JuMP.jl/stable/manual/nonlinear/#Supported-operators)
If you’re still stuck, please start a new thread and we can discusss there.