# Problem with cost function in JuMP

**URL:** <https://discourse.julialang.org/t/problem-with-cost-function-in-jump/36173>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization\
**Created:** [March 19, 2020, 2:34am UTC](https://discourse.julialang.org/t/problem-with-cost-function-in-jump/36173 "2020-03-19T02:34:01Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![mleprovost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mleprovost/32/7166_2.png) [@mleprovost](https://discourse.julialang.org/u/mleprovost)\
**Post date:** [March 19, 2020, 2:34am UTC](https://discourse.julialang.org/t/problem-with-cost-function-in-jump/36173/1 "2020-03-19T02:34:01Z")

</div>

Hello everyone,

I am interested in the following optimization problem that I would like to solve with JuMP:

\begin{split} \min\_{x \in \mathbb{R}^n} & (z^Tx)^2 - \log(b^T x[l:\mbox{end}])\\ \mbox{ subject to }& x[l:\mbox{end}] \geq 0 \end{split}

with k\<n, b \in \mathbb{R}^k and z \in \mathbb{R}^n. x[l:\mbox{end}] denotes the last l components of the vector x.

I am not sure of the way to provide parameters to a user-defined function. Also, I got an error saying that I should use only scalar expressions which seems to be the case

Here is my code:

Code for the cost function

```julia
function _cost(x, wquad, w∂,p)
    J = 0.0
    nx = length(x)
    Ne = size(wquad,2)
    for i=1:Ne
        J += 0.5*sum(wquad[j,i]*x[j] for j=1:nx)^2

        if p==0
        J += -log(w∂[1,i]*x[end])
        else
        J += -log(sum(w∂[j,i]*x[end-(p+2)+j] for j=1:p+2))
        end
    end
    J *= (1/Ne)
    return J
end

```

Rest of the code for the optimization

```julia
p=2
wq = randn(32,200)
w∂ = randn(4,200)

Ne = 200
nx = size(wq,1)
nlog = size(w∂,1)

# Create the model 
model = Model(Ipopt.Optimizer)

# Create variable x
@variable(model, x[1:nx], start = 0.001)

@NLparameter(model, p_order[1]== p)
@NLparameter(model, z[i = 1:nx, j = 1:Ne] == max(wq[i,j], 0.001))
@NLparameter(model, b[i = 1:nlog, j = 1:Ne] == max(w∂[i,j], 0.001))

# Define cost function
cost(x...) = _cost(x, z, b, p_order)
register(model, :cost, 1, cost, autodiff=true)

# Set lower bound on x
for i in nx-nlog:nx
    set_lower_bound(x[i], 0.0)
end

@NLobjective(model, Min, cost(x))

@time optimize!(model)

```

Code return message

```julia
Unexpected array VariableRef[x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12], x[13], x[14], x[15], x[16], x[17], x[18], x[19], x[20], x[21], x[22], x[23], x[24], x[25], x[26], x[27], x[28], x[29], x[30], x[31], x[32]] in nonlinear expression. Nonlinear expressions may contain only scalar expressions.

Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] _parse_NL_expr_runtime(::Model, ::Array{VariableRef,1}, ::Array{JuMP._Derivatives.NodeData,1}, ::Int64, ::Array{Float64,1}) at /Users/me/.julia/packages/JuMP/CZ8vV/src/parse_nlp.jl:207
 [3] top-level scope at /Users/me/.julia/packages/JuMP/CZ8vV/src/parse_nlp.jl:82
 [4] top-level scope at /Users/me/.julia/packages/JuMP/CZ8vV/src/macros.jl:1274
 [5] top-level scope at In[37]:28

```

---

<div class="post-metadata">

**Author:** ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)\
**Post date:** [March 19, 2020, 6:29am UTC](https://discourse.julialang.org/t/problem-with-cost-function-in-jump/36173/2 "2020-03-19T06:29:55Z")

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> [@mleprovost](#):
>
> cost(x…) = \_cost(x, z, b, p\_order)

If you do this, then (I think), `x[1]` will passed as `x`, `x[2]` as `z`, `x[3]` as `b` and `x[4:end]` as `p_order`. Is that what you want?

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<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:** [March 19, 2020, 4:20pm UTC](https://discourse.julialang.org/t/problem-with-cost-function-in-jump/36173/3 "2020-03-19T16:20:09Z")

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Why not just write it out in the macro?

```nohighlight
@NLobjective(model, Min, sum(z[i] * x[i] for i=1:N)^2 - log(sum(b[i] * x[i] for i=l:N)))

```

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<div class="post-metadata">

**Author:** ![mleprovost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mleprovost/32/7166_2.png) [@mleprovost](https://discourse.julialang.org/u/mleprovost)\
**Post date:** [March 20, 2020, 9:43pm UTC](https://discourse.julialang.org/t/problem-with-cost-function-in-jump/36173/4 "2020-03-20T21:43:20Z")

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Thanks I think that’s the way to go. I’ve just found easier to write functions called by others functions.