# JuMP; Rewriting an @eval @NLexpression with a user defined function in local scope w/ Expr

**URL:** <https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757>\
**Category:** Optimization (Mathematical)\
**Created:** [February 1, 2018, 9:52pm UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757 "2018-02-01T21:52:55Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![shoshievass](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shoshievass/32/3260_2.png) [@shoshievass](https://discourse.julialang.org/u/shoshievass)\
**Post date:** [February 1, 2018, 9:52pm UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/1 "2018-02-01T21:52:55Z")

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I’m trying to use a user-defined function that takes in several distinct arguments, and then a splatted N-dim vector of parameters as an @NLexpression to be used in a constraint of an optimization problem.

I described the problem in this thread.

I got the following to work:

```julia
function my_constraint_i(q_b_i, q_b_arr...)
    q_b= [q_b_arr...]
   ....
    STUFF INVOLVING q_b
    constriant_i_out = __function_of_q_b_vector__
   ....
   return constriant_i_out
end

JuMP.register(m, :my_constraint_i, (N+1), my_constraint_i, autodiff=true)
foc_constraint = @eval @NLexpression(m, [i=1:N], my_constraint_i(i, $(q_b...)))
@NLconstraint(m, [i=1:N, foc_constraint[i] == 0)

```

where `my_constraint_i` is a function that takes in an index `i`, and a splatted N-dim vector of parameters and outputs the i’th constraint (for constraining an optimizer w/ a a set of N nonlinear equations in N unknowns).

However, @eval appears to be defined in global scope, and I’m hoping to run the solver inside a function (this is an inner loop of a bigger optimization problem). Is it possible to rewrite this with `Expr`?

The following did not work ☹

```julia
foc_constraint = @NLexpression(m, [i=1:N], Expr(:call, :my_constraint_i, [i, (q_b[j] for j=1:N)...]...))

```

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**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [February 2, 2018, 1:09am UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/2 "2018-02-02T01:09:34Z")

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If you post runnable pieces of code, it will be easier for people to help.

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**Author:** ![miles.lubin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/miles.lubin/32/279_2.png) [@miles.lubin](https://discourse.julialang.org/u/miles.lubin)\
**Post date:** [February 2, 2018, 1:40am UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/3 "2018-02-02T01:40:48Z")

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Any line that contains `@eval @NLexpression` is pretty suspicious. If you need to do anything beyond the syntax that’s supported by `@NLexpression` then you should look at the [raw expression input](http://www.juliaopt.org/JuMP.jl/0.18/nlp.html#raw-expression-input) format. This format lets provide a julia expression object.

This should basically work (haven’t tested it):

```julia
for i in 1:N
    m.addNLconstraint(m, :($(Expr(:call, :my_constraint_i, [i, (q_b[j] for j=1:N)...]...)) == 0))
end

```

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**Author:** ![tkoolen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tkoolen/32/1603_2.png) [@tkoolen](https://discourse.julialang.org/u/tkoolen)\
**Post date:** [February 2, 2018, 1:55am UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/4 "2018-02-02T01:55:51Z")

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Here’s a full example of this kind of thing:

[https://github.com/tkoolen/MotionCaptureJointCalibration.jl/blob/987b9885e6fb83edf5ff61871b636c0b9bc21d31/src/solve.jl#L107](https://github.com/tkoolen/MotionCaptureJointCalibration.jl/blob/987b9885e6fb83edf5ff61871b636c0b9bc21d31/src/solve.jl#L107)

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<div class="post-metadata">

**Author:** ![shoshievass](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shoshievass/32/3260_2.png) [@shoshievass](https://discourse.julialang.org/u/shoshievass)\
**Post date:** [February 2, 2018, 12:50pm UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/5 "2018-02-02T12:50:36Z")

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Thank you guys very much. Your answers have helped me understand a bit more of what’s going on, but @miles.lubin’s suggestion doesn’t quite work and I’m not sure why (I’m getting a Method error saying “no method matching expr\_to\_nodedata”).

Below is a runnable example. The goal is to solve the set of nonlinear equations defined as in the pdf screenshot below (Note: the sum over h^k(s)/(1-H^k(s)) is just a number I’m calling H in the code)

 ![image](https://global.discourse-cdn.com/julialang/original/3X/c/7/c76fd6ab8a5f284ef316a8ced1dc977c4015e6c2.jpeg)

Thank you again for the help!

```julia
using JuMP
using Ipopt
using Parameters

q_a = [3.2, 1.6]
q_o = [2.5, 2.1]
b = [1000, 700]
c = [900, 800]
sigma_t = [0.5, 0.2]
H = [0.000004, 0.000004]

m = Model(solver=IpoptSolver(print_level=5, tol=1e-8))

@variables m begin
    q_b[i=1:length(q_a)]
end

@NLobjective(m, Min, sum((q_b[i] - q_a[i])^2 for i in 1:length(q_a)))

function foc_constraint_i(q_b_i, gamma, q_b_arr...)
    q_b= [q_b_arr...]

    q_b_i = round(Int64, q_b_i)

    b_min_c = b - c
    sigma_sq = sigma_t .* sigma_t

    scaling_factor = (q_o[q_b_i] / gamma) * H[q_b_i]

    variance_utility = exp(-(gamma^2 / 2) * ( (sigma_sq .* b_min_c)' * b_min_c))
    profit_utility = exp(gamma * (dot(q_b, b_min_c)))

    utility = (profit_utility * variance_utility) * scaling_factor

    lhs = q_b[q_b_i] - utility
    rhs = gamma * (sigma_sq[q_b_i] * b_min_c[q_b_i]) - scaling_factor

    constraint_i = lhs - rhs

    return constraint_i
end

foc_constraint_i(100, 0.000001, q_a...) ##Test that this function works

JuMP.register(m, :foc_constraint_i, (2+length(q_a)), foc_constraint_i, autodiff=true)

for i in 1:length(q_a)
    JuMP.addNLconstraint(m, :($(Expr(:call, :foc_constraint_i, [i, 0.00001, (q_b[j] for j=1:length(q_a))...]...)) == 0))
end

status = solve(m)

q_b_min = getvalue(q_b)
answer = getobjectivevalue(m)

```

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<div class="post-metadata">

**Author:** ![shoshievass](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shoshievass/32/3260_2.png) [@shoshievass](https://discourse.julialang.org/u/shoshievass)\
**Post date:** [February 2, 2018, 12:51pm UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/6 "2018-02-02T12:51:41Z")

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I should note that I’ve (eventually) managed to rewrite this without using the function syntax, but I have more complex problems of this sort further into my project and so it would be really helpful to be able to get by with constraints/objectives defined as user-defined functions…

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<div class="post-metadata">

**Author:** ![miles.lubin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/miles.lubin/32/279_2.png) [@miles.lubin](https://discourse.julialang.org/u/miles.lubin)\
**Post date:** [February 4, 2018, 4:07pm UTC](https://discourse.julialang.org/t/jump-rewriting-an-eval-nlexpression-with-a-user-defined-function-in-local-scope-w-expr/8757/7 "2018-02-04T16:07:45Z")

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> [@shoshievass](#):
>
> ```julia
> for i in 1:length(q_a)
> JuMP.addNLconstraint(m, :($(Expr(:call, :foc_constraint_i, [i, 0.00001, (q_b[j] for j=1:length(q_a))...]...)) == 0))
> end
> 
> ```

The following seems to work instead:

```julia
for i in 1:length(q_a)
    JuMP.addNLconstraint(m, :($(Expr(:call, :foc_constraint_i, i, 0.00001, (q_b[j] for j=1:length(q_a))...)) == 0))
end

```