# (Interval) subset optimization with JuMP

**URL:** <https://discourse.julialang.org/t/interval-subset-optimization-with-jump/30415>\
**Category:** Optimization (Mathematical)\
**Created:** [October 28, 2019, 7:06pm UTC](https://discourse.julialang.org/t/interval-subset-optimization-with-jump/30415 "2019-10-28T19:06:31Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![joemiller](https://avatars.discourse-cdn.com/v4/letter/j/258eb7/32.png) [@joemiller](https://discourse.julialang.org/u/joemiller)\
**Post date:** [October 28, 2019, 7:06pm UTC](https://discourse.julialang.org/t/interval-subset-optimization-with-jump/30415/1 "2019-10-28T19:06:31Z")

</div>

Hey everyone. I’m trying to figure out how to use JuMP to optimize a function of a slice of data over the left and right endpoints for the range.

I’ve never used JuMP before so I’m piecing this together from tutorials and the docs.

```julia
# data
x = randn(100)

# func to optimize
mysum(left, right, x = x) = sum(x[left:right])

m = Model()
@variable(m, left, lower_bound = 1, upper_bound = length(x))
@variable(m, right, lower_bound = 1, upper_bound = length(x))

@constraint(m, left + 20 <= right)
@constraint(m, left in MOI.Integer())
@constraint(m, right in MOI.Integer())

@objective(m, Max, mysum(left, right))

```

I get `ERROR: MethodError: no method matching isless(::GenericAffExpr{Float64,VariableRef}, ::GenericAffExpr{Float64,VariableRef})`

What am I doing wrong? What’s the correct way to specify this type of optimization problem?

Appreciate the help!

P.S. I tried rewriting

```julia
function mysum(left, right, x)
    x_sub = [el for (i,el) in enumerate(x) if left ≤ i ≤ right]
    sum(x_sub)
end

```

but it yields the same error.

---

<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:** [October 28, 2019, 7:17pm UTC](https://discourse.julialang.org/t/interval-subset-optimization-with-jump/30415/2 "2019-10-28T19:17:34Z")

</div>

You can’t use the value of a variable (e.g., `left`) inside a splice.

You should re-formulate your model like so (n.b., I haven’t tested this, so there might be bugs):

```nohighlight
x = rand(100)
model = Model()
@variable(model, 1 <= left <= 100, Int)
@variable(model, 1 <= right <= 100, Int)
@variable(model, z[1:100], Bin)
@constraint(model, left + 20 <= right)
@constraint(model, [i = 1:100], (101 - i) * z[i] <= 101 - left)
@constraint(model, [i = 1:100], i * z[i] <= right)
@objective(model, Max, sum(x[i] * z[i] for i in 1:100))

```

---

<div class="post-metadata">

**Author:** ![joemiller](https://avatars.discourse-cdn.com/v4/letter/j/258eb7/32.png) [@joemiller](https://discourse.julialang.org/u/joemiller)\
**Post date:** [October 28, 2019, 7:50pm UTC](https://discourse.julialang.org/t/interval-subset-optimization-with-jump/30415/3 "2019-10-28T19:50:01Z")

</div>

Thanks! I had to add the following constraint to your answer to ensure that we don’t get solutions like `[0,0,1,1,1,0,1]`

```julia
@constraint(model, sum(z) == right - left + 1)

```