# Set depending of an index

**URL:** <https://discourse.julialang.org/t/set-depending-of-an-index/42322>\
**Category:** Optimization (Mathematical)\
**Created:** [June 30, 2020, 7:34pm UTC](https://discourse.julialang.org/t/set-depending-of-an-index/42322 "2020-06-30T19:34:08Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![angeloaliano1](https://avatars.discourse-cdn.com/v4/letter/a/7ea924/32.png) [@angeloaliano1](https://discourse.julialang.org/u/angeloaliano1)\
**Post date:** [June 30, 2020, 7:34pm UTC](https://discourse.julialang.org/t/set-depending-of-an-index/42322/1 "2020-06-30T19:34:08Z")

</div>

Dear all,  
I have a constraint in a integer program like

```julia
@constraint(modelo,[j in J,i in I],
    sum(x[i,k,h] for h in H for k in S_j) <= 1
)

```

My problem is how can I write this constraint by using the set S\_j.  
For example, if j=1, then S\_j = {2,4}, if j=2, S\_j = {1,3,4}, if j=3 S\_j = {2,5,6} and so on, for each j I have a S\_j with a diferent cardinality.  
Best regards.

---

<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:** [June 30, 2020, 7:41pm UTC](https://discourse.julialang.org/t/set-depending-of-an-index/42322/2 "2020-06-30T19:41:33Z")

</div>

```nohighlight
S = [[2, 4], [1, 3, 4], [2, 5, 6]]
model = Model()
@variable(model, x[1:6])
@constraint(model, [j in 1:3], sum(x[k] for k in S[j]) <= 1)

```