# @constraint with ForwardDiff.gradient

**URL:** <https://discourse.julialang.org/t/constraint-with-forwarddiff-gradient/104949>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, forwarddiff\
**Created:** [October 14, 2023, 10:34am UTC](https://discourse.julialang.org/t/constraint-with-forwarddiff-gradient/104949 "2023-10-14T10:34:17Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![justinberi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/justinberi/32/202466_2.png) [@justinberi](https://discourse.julialang.org/u/justinberi)\
**Post date:** [October 14, 2023, 10:34am UTC](https://discourse.julialang.org/t/constraint-with-forwarddiff-gradient/104949/1 "2023-10-14T10:34:17Z")

</div>

Hi All,

Thanks in advance for any help and suggestions. I’m new to Julia (and JuMP) so go easy.

Is there a way to use `ForwardDiff.gradient` within a nonlinear constraint in JuMP?

An example is

```julia
# Solve using JuMP interface to Ipopt
import JuMP # v1.15.1
import Ipopt
import ForwardDiff as FD

# Suggested by compiler, didn't work
# FD.can_dual(::Type{JuMP.AffExpr}) = true

### Avoid modification ###
Q = [1.65539 2.89376; 2.89376 6.51521];
q = [2;-3]

f(x) = 0.5*x'*Q*x + q'*x + exp(-1.3*x[1] + 0.3*x[2]^2)
function kkt_conditions(x)
    return FD.gradient(f,x)
end
residual_fx(_x) = kkt_conditions(_x)

# Initial condition
x0 = [-0.9512129986081451, 0.8061342694354091]
######

model = JuMP.Model(Ipopt.Optimizer)

# Helpers suggested in https://jump.dev/JuMP.jl/stable/manual/nonlinear/ 
my_fun(x...) = residual_fx(collect(x))
JuMP.@operator(model, op_f, 5, (x...) -> residual_fx(collect(x)))

# Solver setup
JuMP.@variable(model, x[i=1:2], start = x0[i])

## Tried 
# JuMP.@constraint(model, my_fun(x...) .== 0) # MethodError: Cannot `convert` an object of type JuMP.AffExpr to an object of type JuMP.VariableRef
# JuMP.@constraint(model, op_f(x...) == 0) # MethodError: no method matching length(::JuMP.NonlinearExpr)

# Ideally this would be the best syntax
JuMP.@constraint(model, residual_fx(x) .== 0) # MethodError: Cannot `convert` an object of type JuMP.AffExpr to an object of type JuMP.VariableRef

# Solve
JuMP.optimize!(model)

print("Residual: ", residual_fx(JuMP.value.(x)))

```

This results in

```julia
MethodError: Cannot `convert` an object of type JuMP.AffExpr to an object of type JuMP.VariableRef

Closest candidates are:
  convert(::Type{T}, ::T) where T
   @ Base Base.jl:64
  (::Type{JuMP.GenericVariableRef{T}} where T)(::Any, ::Any)
   @ JuMP ~/.julia/packages/JuMP/ToPd2/src/variables.jl:243

Stacktrace:
  [1] cvt1
    @ ./essentials.jl:418 [inlined]
  [2] ntuple
    @ ./ntuple.jl:49 [inlined]
  [3] convert(#unused#::Type{Tuple{JuMP.VariableRef, JuMP.VariableRef}}, x::Tuple{JuMP.AffExpr, JuMP.AffExpr})
    @ Base ./essentials.jl:419
  [4] ForwardDiff.Partials{2, JuMP.VariableRef}(values::Tuple{JuMP.AffExpr, JuMP.AffExpr})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/partials.jl:2
  [5] convert(#unused#::Type{ForwardDiff.Partials{2, JuMP.VariableRef}}, partials::ForwardDiff.Partials{2, JuMP.AffExpr})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/partials.jl:74
  [6] cvt1
    @ ./essentials.jl:418 [inlined]
  [7] ntuple(f::Base.var"#cvt1#1"{Tuple{ForwardDiff.Partials{2, JuMP.VariableRef}, ForwardDiff.Partials{2, JuMP.VariableRef}}, Tuple{ForwardDiff.Partials{2, JuMP.AffExpr}, ForwardDiff.Partials{2, JuMP.AffExpr}}}, #unused#::Val{2})
    @ Base ./ntuple.jl:49
  [8] convert
    @ ./essentials.jl:419 [inlined]
  [9] GradientConfig
    @ ~/.julia/packages/ForwardDiff/PcZ48/src/config.jl:98 [inlined]
 [10] ForwardDiff.GradientConfig(f::typeof(f), x::Vector{JuMP.VariableRef}, ::ForwardDiff.Chunk{2}, ::ForwardDiff.Tag{typeof(f), JuMP.VariableRef})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/config.jl:123
 [11] ForwardDiff.GradientConfig(f::typeof(f), x::Vector{JuMP.VariableRef}, ::ForwardDiff.Chunk{2})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/config.jl:121
 [12] ForwardDiff.GradientConfig(f::typeof(f), x::Vector{JuMP.VariableRef})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/config.jl:121
 [13] gradient(f::Function, x::Vector{JuMP.VariableRef})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/gradient.jl:17
 [14] kkt_conditions
    @ ./In[41]:19 [inlined]
 [15] residual_fx(_x::Vector{JuMP.VariableRef})
    @ Main ./In[56]:17
 [16] macro expansion
    @ ~/.julia/packages/MutableArithmetics/K9YPJ/src/rewrite.jl:321 [inlined]
 [17] macro expansion
    @ ~/.julia/packages/JuMP/ToPd2/src/macros.jl:717 [inlined]
 [18] top-level scope
    @ In[56]:37

```

Many of the use cases I am looking at have 3rd party provided vectorised constraint functions. So any solutions that minimally change the user provided constraints would be amazing, if it’s possible.

Possibly linked to [ForwardDiff: Error ForwardDiff.Tag How to transform a Dual Type to a Float](https://discourse.julialang.org/t/forwarddiff-error-forwarddiff-tag-how-to-transform-a-dual-type-to-a-float/45884)

---

<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:** [October 15, 2023, 9:57pm UTC](https://discourse.julialang.org/t/constraint-with-forwarddiff-gradient/104949/2 "2023-10-15T21:57:01Z")

</div>

Hi @justinberi, welcome to the forum.

You’re running into a couple of issues:

- After registering an operator, you need to use `op_f` instead of `residual_fx`
- You need to get the input number of arguments correct
- You need to splat the input to `op_f(x...)`

But those are relatively minor. A bigger block is that operators must return a scalar, whereas yours returns a vector. One solution is:

```julia
import JuMP
import Ipopt
import ForwardDiff as FD
Q = [1.65539 2.89376; 2.89376 6.51521];
q = [2; -3]
f(x) = 0.5*x'*Q*x + q'*x + exp(-1.3*x[1] + 0.3*x[2]^2)
kkt_conditions(x) = FD.gradient(f,x)
residual_fx(_x) = kkt_conditions(_x)
x0 = [-0.9512129986081451, 0.8061342694354091]
model = JuMP.Model(Ipopt.Optimizer)
JuMP.@operator(model, op_f1, 2, (x...) -> residual_fx(collect(x))[1])
JuMP.@operator(model, op_f2, 2, (x...) -> residual_fx(collect(x))[2])
JuMP.@variable(model, x[i=1:2], start = x0[i])
JuMP.@constraint(model, op_f1(x...) == 0)
JuMP.@constraint(model, op_f2(x...) == 0)
JuMP.optimize!(model)

```

If performance is an issue, you can implement this work-around:

> **[Tips and tricks · JuMP](https://jump.dev/JuMP.jl/stable/tutorials/nonlinear/tips_and_tricks/#User-defined-operators-with-vector-outputs)**
>
> Documentation for JuMP.

---

<div class="post-metadata">

**Author:** ![justinberi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/justinberi/32/202466_2.png) [@justinberi](https://discourse.julialang.org/u/justinberi)\
**Post date:** [October 16, 2023, 1:04pm UTC](https://discourse.julialang.org/t/constraint-with-forwarddiff-gradient/104949/3 "2023-10-16T13:04:02Z")

</div>

Hey @odow, thanks for your help and the effort you are putting into a great community and package!

That solves the issue I was having.

Inevitably it brought up more questions but I will ask them in separate topics and link here.

---

<div class="post-metadata">

**Author:** ![justinberi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/justinberi/32/202466_2.png) [@justinberi](https://discourse.julialang.org/u/justinberi)\
**Post date:** [October 16, 2023, 1:05pm UTC](https://discourse.julialang.org/t/constraint-with-forwarddiff-gradient/104949/4 "2023-10-16T13:05:56Z")

</div>

[What is the difference between nonlinear “functions with vector outputs” and nonlinear “operators with vector outputs”?](https://discourse.julialang.org/t/what-is-the-difference-between-nonlinear-functions-with-vector-outputs-and-nonlinear-operators-with-vector-outputs/105012)