# JuMP constraints with conditions in Sum

**URL:** https://discourse.julialang.org/t/jump-constraints-with-conditions-in-sum/11059
**Category:** General Usage
**Tags:** question
**Created:** [May 21, 2018, 9:46pm UTC](https://discourse.julialang.org/t/jump-constraints-with-conditions-in-sum/11059 "2018-05-21T21:46:10Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![majbah](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@majbah](https://discourse.julialang.org/u/majbah)
#### Post date: [May 21, 2018, 9:46pm UTC](https://discourse.julialang.org/t/jump-constraints-with-conditions-in-sum/11059/1 "2018-05-21T21:46:10Z")

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I am trying to solve an optimization problem with JuMP. Is there any way to include “condition” in the “sum” part of `@constraint` macro?

The constraint is: \sum\_{c \in C} \sum\_{s \in S} \sum\_{r \in S, s \ne r} (x\_s^c + 2 \* y\_sr^c) = S

My code:` @constraint(m, sum((x[s,c] + 2 * y[s,r,c]) for s=1:length(routes), r=1:length(routes), c=1:length(carrier)) == length(routes))`

How can I include “s \ne r” condition in the `@constraint` macro?

Thanks!

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### 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: [May 21, 2018, 10:00pm UTC](https://discourse.julialang.org/t/jump-constraints-with-conditions-in-sum/11059/2 "2018-05-21T22:00:56Z")

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JuMP `sum`s use standard [Julia generator syntax](https://docs.julialang.org/en/stable/manual/arrays/#Generator-Expressions-1). So you can go:

```julia
julia> using JuMP

julia> m=Model()
Feasibility problem with:
 * 0 linear constraints
 * 0 variables
Solver is default solver

julia> @variable(m, x[1:3])
3-element Array{JuMP.Variable,1}:
 x[1]
 x[2]
 x[3]

julia> @constraint(m, sum(x[i] for i in 1:3 if i != 2) == 1)
x[1] + x[3] == 1

```

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<div class="post-metadata">

### Author: ![majbah](https://avatars.discourse-cdn.com/v4/letter/m/a5b964/32.png) [@majbah](https://discourse.julialang.org/u/majbah)
#### Post date: [May 22, 2018, 6:25pm UTC](https://discourse.julialang.org/t/jump-constraints-with-conditions-in-sum/11059/3 "2018-05-22T18:25:04Z")

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Thank you for the help.
