# JuMP sum variables with arbitrary set of indices

**URL:** <https://discourse.julialang.org/t/jump-sum-variables-with-arbitrary-set-of-indices/7024>\
**Category:** Optimization (Mathematical)\
**Created:** [November 12, 2017, 11:54am UTC](https://discourse.julialang.org/t/jump-sum-variables-with-arbitrary-set-of-indices/7024 "2017-11-12T11:54:45Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![Rafal\_Machalica](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafal_machalica/32/8207_2.png) [@Rafal\_Machalica](https://discourse.julialang.org/u/Rafal_Machalica)\
**Post date:** [November 12, 2017, 11:54am UTC](https://discourse.julialang.org/t/jump-sum-variables-with-arbitrary-set-of-indices/7024/1 "2017-11-12T11:54:45Z")

</div>

Hello,

I’m trying to write a constraint with sum of variables with irregular indexes pattern.

With regular indices it works fine:

```julia
using JuMP
m = Model()
@variable(m, x[1:100, 1:100])
@constraint(m, sum(x[i, j] for i = 1:5, j = 7:13) == 87)
println(m)

```

resulting in following output:

```julia
 x[1,7] + x[1,8] + x[1,9] + x[1,10] + x[1,11] + x[1,12] + x[1,13] + x[2,7] + x[2,8] + x[2,9] + x[2,10] + x[2,11] + x[2,12] + x[2,13] + x[3,7] + x[3,8] + x[3,9] + x[3,10] + x[3,11] + x[3,12] + x[3,13] + x[4,7] + x[4,8] + x[4,9] + x[4,10] + x[4,11] + x[4,12] + x[4,13] + x[5,7] + x[5,8] + x[5,9] + x[5,10] + x[5,11] + x[5,12] + x[5,13] == 87

```

Now, I want to create constraint with more complicated pattern of indexes, lets’ say

```julia
[13,4], [22,78], [18,97], [56,32]

```

so that my constraint would look like this:

```julia
x[13,4] + x[22,78] + x[18,97] + x[56,32] == 87

```

I have an array “a” of indexes and I try to do something like this:

```julia
using JuMP
m = Model()
@variable(m, x[1:100, 1:100])
a = [[13,4], [22,78], [18,97], [56,32]]
@constraint(m, sum(x[i] for i in a) == 87)
println(m)

```

but it doesn’t work:

```julia
ERROR: LoadError: The operators <=, >=, and == can only be used to specify scalar constraints. If you are trying to add a vectorized constraint, use the element-wise dot comparison operators (.<=, .>=, or .==) instead

```

I don’t want to create vectorized constraint. I want a single scalar constraint with arbitrary variable indexes predefined in an array (or whatever else). Any suggestions please?

---

<div class="post-metadata">

**Author:** ![abulak](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/abulak/32/28314_2.png) [@abulak](https://discourse.julialang.org/u/abulak)\
**Post date:** [November 12, 2017, 12:00pm UTC](https://discourse.julialang.org/t/jump-sum-variables-with-arbitrary-set-of-indices/7024/2 "2017-11-12T12:00:04Z")

</div>

> [@Rafal\_Machalica](#):
>
> using JuMP  
> m = Model()  
> @variable(m, x[1:100, 1:100])  
> a = [[13,4], [22,78], [18,97], [56,32]]  
> @constraint(m, sum(x[i] for i in a) == 87)  
> println(m)

Try `@expression(m, sum(x[i,j] for (i,j) in a))`

---

<div class="post-metadata">

**Author:** ![Rafal\_Machalica](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafal_machalica/32/8207_2.png) [@Rafal\_Machalica](https://discourse.julialang.org/u/Rafal_Machalica)\
**Post date:** [November 12, 2017, 12:10pm UTC](https://discourse.julialang.org/t/jump-sum-variables-with-arbitrary-set-of-indices/7024/3 "2017-11-12T12:10:56Z")

</div>

That did the trick. It works even without involving @expression.

```julia
@constraint(m, sum(x[i,j] for (i,j) in a) == 87)

```

works as well.

Thank you for prompt and informative answer.

---

<div class="post-metadata">

**Author:** ![abulak](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/abulak/32/28314_2.png) [@abulak](https://discourse.julialang.org/u/abulak)\
**Post date:** [November 12, 2017, 12:55pm UTC](https://discourse.julialang.org/t/jump-sum-variables-with-arbitrary-set-of-indices/7024/4 "2017-11-12T12:55:54Z")

</div>

`@expression` just builds a JuMP expression which can be used to define different types of constraints;

Note if the index set `a` contains duplicates JuMP will not “compress”, or rather compile the expression before handling them to the actual solver, which my lead to high memory use. In one of my problems I had to “compactify” the constraints manually.