# Build NLexpression in steps

**URL:** <https://discourse.julialang.org/t/build-nlexpression-in-steps/15199>\
**Category:** Optimization (Mathematical)\
**Tags:** question\
**Created:** [September 19, 2018, 9:48pm UTC](https://discourse.julialang.org/t/build-nlexpression-in-steps/15199 "2018-09-19T21:48:52Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![jacob-roth](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jacob-roth/32/1862_2.png) [@jacob-roth](https://discourse.julialang.org/u/jacob-roth)\
**Post date:** [September 19, 2018, 9:48pm UTC](https://discourse.julialang.org/t/build-nlexpression-in-steps/15199/1 "2018-09-19T21:48:52Z")

</div>

I want to build an `NLexpression` which is the sum of elements of an array containing both `JuMP` variables and `Float64`s, something like:

```julia
model = Model()
@variable(model, x[1:2])
xx = [x[1]; 3.0; 4.0; 5.0; x[2]]
@NLexpression(model, test, sin(xx[1]))
for i = 2:5
    aux = @NLexpression(model, sin(xx[i]))
    test += aux
end

```

Is it possible to “build up” a single nonlinear expression in steps like this? I’m hoping for a cleaner way to do it than to create three separate `NLexpressions`: two to handle the variable and constant parts separately and one to combine them. I might be missing something obvious…

I can do this for `expression`s as:

```julia
model = Model()
@variable(model, x[1:2])
xx = [x[1]; 3.0; 4.0; 5.0; x[2]]
@expression(model, test, (xx[1]))
for i = 2:5
    aux = @expression(model, (xx[i]))
    test += aux
end

```

---

<div class="post-metadata">

**Author:** ![jacob-roth](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jacob-roth/32/1862_2.png) [@jacob-roth](https://discourse.julialang.org/u/jacob-roth)\
**Post date:** [October 19, 2018, 5:12pm UTC](https://discourse.julialang.org/t/build-nlexpression-in-steps/15199/2 "2018-10-19T17:12:50Z")

</div>

This works: define an `N`-dim array `xx = Array{Union{Float64, JuMP.Variable},1}(N)` first and then fill.

Example:

```julia
using JuMP, Ipopt
N = 10
x0 = rand(N);

A = rand(N,N); A = A'*A
b = rand(N)
x_true = A\b
vlist = [1,3,5,7,9]; Nv = length(vlist)
plist = [2,4,6,8,10]; Np = length(plist)
x0[plist] = x_true[plist]

## -----------------------------------------------------------------------------
xp = x0[plist]
test = Model(solver=IpoptSolver())
@variable(test, xvar[vlist])
x_combined = Array{Union{Float64, JuMP.Variable}, 1}(10)
for i in vlist
    x_combined[i] = xvar[i]
end
x_combined[plist] = xp
@NLexpression(test, xAx, sum(
                            sum(
                                0.5*x_combined[i]*x_combined[j]*A[i,j]
                            for i=1:N)
                         for j=1:N)
 )
@NLobjective(test, Min, xAx - sum(b[i] * x_combined[i] for i=1:N))

## -----------------------------------------------------------------------------
solve(test)
xvar_star = getvalue(test[:xvar])
x_star = zeros(N)
x_star[plist] = xp

for i in vlist
    x_star[i] = xvar_star[i]
end
A*x_star - b

```