# Cannot register function because it does not support differentiation although it does

**URL:** <https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [June 22, 2022, 8:31am UTC](https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167 "2022-06-22T08:31:00Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![DanDoe](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dandoe/32/52717_2.png) [@DanDoe](https://discourse.julialang.org/u/DanDoe)\
**Post date:** [June 22, 2022, 8:31am UTC](https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167/1 "2022-06-22T08:31:00Z")

</div>

I want to perform some nonlinear optimization using `Ipopt` through `JuMP`.

I have some user-defined function `p_nomr_ln_Sum` (see below) that I want to use throughout the optimization. I keep getting the error `ERROR: LoadError: Unable to register the function :p_norm_ln_Sum because it does not support differentiation via ForwardDiff.` I followed the debug instruction of JuMP and tested my function with `ForwardDiff.jl` alone and it works just as intended.

Here’s the code:

```julia
using JuMP, Ipopt
using ForwardDiff

# Some dummy parameters
dt = 42.0;
p = 2;
NumStageEvals = 1;
NumEigVals = 2;
RealEigVals = [42.0, 42.0];
ImagEigVals = [42.0, 42.0];

# To my understanding, `T` is the type needed to overload the computations to compute the derivative.
# This is why I use it only for the variables.
function p_norm_ln_Sum(x::Vector{T}, dt::Float64, p::Int, NumStageEvals::Int, 
                       NumEigVals::Int, RealEigVals::Vector{Float64}, 
                       ImagEigVals::Vector{Float64}) where {T<:Real}

  ln_Sums = zeros(T, NumEigVals);

  for j in 1:NumStageEvals
    ln_Sums[:] += log.( (1 .- x[2*j-1]*dt*RealEigVals[:] + x[2*j]*dt*ImagEigVals[:]).^2 
                       + (x[2*j-1]*dt*ImagEigVals[:] + x[2*j]*dt*RealEigVals[:]).^2)
  end

  return sum(ln_Sums[i]^p for i in 1:NumEigVals)^(1.0/p)
end

x = [42.0, 42.0]; # Some values
# Works perfectly
y = ForwardDiff.gradient(x->p_norm_ln_Sum(x, dt, p, NumStageEvals, NumEigVals, RealEigVals, ImagEigVals), x)
display(y); println() # Gives some meaningful output

model = Model(Ipopt.Optimizer)

# Does not work
register(model, :p_norm_ln_Sum, 7, p_norm_ln_Sum; autodiff=true) 

```

The whole error message is:

```julia
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:33
 [2] _validate_register_assumptions(f::typeof(p_norm_ln_Sum), name::Symbol, dimension::Int64)
   @ JuMP ~/.julia/packages/JuMP/Y4piv/src/nlp.jl:1979
 [3] register(m::Model, s::Symbol, dimension::Int64, f::Function; autodiff::Bool)
   @ JuMP ~/.julia/packages/JuMP/Y4piv/src/nlp.jl:2052
 [4] top-level scope
   @ ~/Desktop/git/MA/Optim_Julia/Opt_Roots.jl:31
in expression starting at /Optim_Julia/Opt_Roots.jl:31

caused by: MethodError: no method matching p_norm_ln_Sum(
::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7},
 ::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7},
 ::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7},
 ::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7},
 ::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7}, 
 ::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7},
 ::ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7})

Stacktrace:
 [1] (::JuMP.var"#142#143"{typeof(p_norm_ln_Sum(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"
{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7}})
   @ JuMP ~/.julia/packages/JuMP/Y4piv/src/nlp.jl:1975
 [2] vector_mode_dual_eval!(f::JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7}}}, x::Vector{Float64})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/wAaVJ/src/apiutils.jl:37
 [3] vector_mode_gradient(f::JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7}}})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/wAaVJ/src/gradient.jl:106
 [4] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7}}}, ::Val{true})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/wAaVJ/src/gradient.jl:19
 [5] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{JuMP.var"#142#143"{typeof(p_norm_ln_Sum)}, Float64}, Float64, 7}}}) (repeats 2 times)
   @ ForwardDiff ~/.julia/packages/ForwardDiff/wAaVJ/src/gradient.jl:17
 [6] _validate_register_assumptions(f::typeof(p_norm_ln_Sum), name::Symbol, dimension::Int64)
   @ JuMP ~/.julia/packages/JuMP/Y4piv/src/nlp.jl:1975
 [7] register(m::Model, s::Symbol, dimension::Int64, f::Function; autodiff::Bool)
   @ JuMP ~/.julia/packages/JuMP/Y4piv/src/nlp.jl:2052
 [8] top-level scope

```

---

<div class="post-metadata">

**Author:** ![tomaklutfu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomaklutfu/32/2411_2.png) [@tomaklutfu](https://discourse.julialang.org/u/tomaklutfu)\
**Post date:** [June 22, 2022, 8:49am UTC](https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167/2 "2022-06-22T08:49:50Z")

</div>

While `ForwardDiff` only takes gradient with respect to `x`, `JuMP` tries to differentiate with repect to all the inputs. If you change your model to use it like `ForwardDiff` usage it can be used AFAIK.

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 22, 2022, 8:55am UTC](https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167/3 "2022-06-22T08:55:31Z")

</div>

See the documentation: [Nonlinear Modeling · JuMP](https://jump.dev/JuMP.jl/stable/manual/nlp/#User-defined-functions-with-vector-inputs)

You cannot provide a vector as input.

---

<div class="post-metadata">

**Author:** ![DanDoe](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dandoe/32/52717_2.png) [@DanDoe](https://discourse.julialang.org/u/DanDoe)\
**Post date:** [June 22, 2022, 9:26am UTC](https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167/4 "2022-06-22T09:26:12Z")

</div>

Hm, do you know of any guidance/tutorial how to use functions in `JuMP` that take vector-valued decision variables together with vector-valued parameters? To my understanding, I would now need to construct cascades of theses splatted functions to resemble my function as written above.

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 22, 2022, 9:14pm UTC](https://discourse.julialang.org/t/cannot-register-function-because-it-does-not-support-differentiation-although-it-does/83167/5 "2022-06-22T21:14:41Z")

</div>

> how to use functions in `JuMP` that take vector-valued decision variables together with vector-valued parameters?

You cannot. You can only use functions which take scalar variables as arguments.

In your case, you might create a new function like:

```julia
(x...) -> p_norm_ln_Sum(collect(x), dt, p, ...)

```