# Find dependent variables as GenericAffExpr

**URL:** <https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [September 3, 2020, 1:46pm UTC](https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009 "2020-09-03T13:46:00Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![umbe](https://avatars.discourse-cdn.com/v4/letter/u/f19dbf/32.png) [@umbe](https://discourse.julialang.org/u/umbe)\
**Post date:** [September 3, 2020, 1:46pm UTC](https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009/1 "2020-09-03T13:46:00Z")

</div>

Hi everybody!  
I’m trying to find a way to obtain the dependent variables of a nonlinear system as GenericAffExpr, expressed as a function only of the independent variables of an optimization problem.

To be more precise, I have a nonlinear problem with independent variables x. The objective function is a function of both x and other dependent variables y. In order to compute the OF, is necessary to obtain the expressions of y in function of x (in type GenericAffExpr, I suppose).  
These y can be found by solving a nonlinear system of equations and to do that, I wrote a second optimization model that (in my intentions) should execute this task.

To be clearer, below is reported a minimal example of what I would like to do.

```julia
using JuMP, Ipopt

# define optimization problem with independent variables (x)
m = Model(Ipopt.Optimizer)
@variable(m, x[1:2])

# solve nonlinear system to find dependent variables (y)
p = Model(Ipopt.Optimizer)
@variable(p, y[1:2])
@NLconstraint(p, x[1] * y[1] * y[2] == 2)
@NLconstraint(p, x[2] * y[1] * y[2] == 5)
@objective(p, 0.0)
JuMP.optimize!(p)

# solve original problem
@NLobjective(m, x[1] + x[2]^2 + sum(y))
JuMP.optimize!(m)

```

However, trying to define the ‘inner’ optimization p, JuMP provides the error **Variable in nonlinear expression does not belong to the corresponding model** in correspondence of the first @NLconstraint, since the variables x are inserted in the problem p but belong to the problem m.

My question is: does anyone know if exist a suitable way to solve this issue? Or, does exist another strategy to reach my purpose?

Thank you in advance for your help.

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 3, 2020, 2:16pm UTC](https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009/2 "2020-09-03T14:16:43Z")

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I’m guessing you want to extract the value of `y` that you found after solving `p`? If so,

```julia
@NLobjective(m, x[1] + x[2]^2 + sum(value.(y)))

```

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<div class="post-metadata">

**Author:** ![umbe](https://avatars.discourse-cdn.com/v4/letter/u/f19dbf/32.png) [@umbe](https://discourse.julialang.org/u/umbe)\
**Post date:** [September 3, 2020, 4:16pm UTC](https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009/3 "2020-09-03T16:16:16Z")

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In a certain sense yes, but, since the variables x are present in the problem p and the problem p only optimize the variables y, the values of y should contain the terms of x. In other words, I would like that the problem p has the following outputs:

```julia
y[1] = (10 / (x[1] * x[2]))^0.5
y[2] = ((5 / 2) * x[1] / x[2])^0.5

```

And the type of y should be Array{GenericAffExpr{Float64,VariableRef},1}.

However, to get the value.(y) that you suggested, I have to run the inner optimization (problem p), which is the one that is giving me problems.

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 3, 2020, 4:24pm UTC](https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009/4 "2020-09-03T16:24:57Z")

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Ah, ok, I took another look and you’re right that wouldn’t work. You can’t mix-and-match variables and models this way. The thing to do is use a single model that contains all the necessary variables (you can add/delete constraints/variables and change the objective as necessary).

```julia
m = Model(Ipopt.Optimizer)
@variable(m, x[1:2])
@variable(m, y[1:2])
c1 = @NLconstraint(m, x[1] * y[1] * y[2] == 2)
c2 = @NLconstraint(m, x[2] * y[1] * y[2] == 5)
@objective(m, 0.0) # (note this isn't necessary)
JuMP.optimize!(m)
# should you check termination_status(m) before proceeding?

# solve original problem:
# get rid of the constraints if they don't matter any more
delete!.(m, (c1, c2))
@NLobjective(m, x[1] + x[2]^2 + sum(value.(y)))
JuMP.optimize!(m)

```

Alternatively, you could create a new model with only variables called `x` and set its objective based on the other model’s value for `y`.

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<div class="post-metadata">

**Author:** ![umbe](https://avatars.discourse-cdn.com/v4/letter/u/f19dbf/32.png) [@umbe](https://discourse.julialang.org/u/umbe)\
**Post date:** [September 4, 2020, 7:56am UTC](https://discourse.julialang.org/t/find-dependent-variables-as-genericaffexpr/46009/5 "2020-09-04T07:56:27Z")

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Ok, thank you very much, I’ll try your suggestions!