# 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:** 1
**Showing post:** 5

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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 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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