# Abs in JuMP
**URL:** https://discourse.julialang.org/t/abs-in-jump/90811
**Category:** Optimization (Mathematical)
**Tags:** question, jump
**Created:** [November 25, 2022, 2:06pm UTC](https://discourse.julialang.org/t/abs-in-jump/90811 "2022-11-25T14:06:17Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@Salvador\_Catsis](https://discourse.julialang.org/u/Salvador_Catsis)
#### Post date: [November 25, 2022, 2:06pm UTC](https://discourse.julialang.org/t/abs-in-jump/90811/1 "2022-11-25T14:06:17Z")
Hi,
I’m fairly new to Julia and new to JuMP. I am trying to implement a simple optimisation problem. I haven’t asked many programming questions before so please forgive the formatting if it’s not appropriate.
I have defined a matrix S where each row is a shifted exponential with a negative exponent and the vector x is the target vector. I want to choose the optimal weighting of these shifted exponentials to minimise the absolute distance to x. After looking at a few similar questions, I have defined 4 binary vectors for each of the 4 weights 50, 25, 12.5 and 0. The issue is that I can’t take the absolute value of the difference. I think I need to do something like
expression[i] \<= x[i]
-expression[i] \<= x[i]
but I’m not sure exactly how to implement that there.
The code I have so far is
```julia
model = Model(HiGHS.Optimizer)
@variable(model, A[i=1:N], Bin)
@variable(model, B[i=1:N], Bin)
@variable(model, C[i=1:N], Bin)
@variable(model, D[i=1:N], Bin)
for i in range(1, N)
@constraint(model, A[i] + B[i] + C[i] + D[i] == 1)
end
@objective(
model,
Min,
sum(sum(S[i, :].*(A[i] * 50 + B[i] * 25 + C[i] * 12.5 + D[i] * 0) for i in 1:N-1) .- x)
)
```
Thanks
---
### Author:  [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)
#### Post date: [November 25, 2022, 2:16pm UTC](https://discourse.julialang.org/t/abs-in-jump/90811/2 "2022-11-25T14:16:17Z")
This is not really JuMP/Julia-specific, but a common problem for linear programming, you can find the general trick to do absolutes in linear programs in [Converting absolute value program into linear program - Mathematics Stack Exchange](https://math.stackexchange.com/questions/432003/converting-absolute-value-program-into-linear-program)
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [November 26, 2022, 4:51am UTC](https://discourse.julialang.org/t/abs-in-jump/90811/3 "2022-11-26T04:51:02Z")
> [@Salvador\_Catsis](#):
>
> I’m fairly new to Julia and new to JuMP
Hi!
> I haven’t asked many programming questions before so please forgive the formatting if it’s not appropriate.
It’s a good question. You can make it a little better by providing the `S` and `x` matrices. Currently, I can’t run your example.
To model `abs`, you can use:
```julia
# To model: sum(abs.(y .- x))
@variable(model, t[1:length(x)] >= 0)
@constraint(model, t .>= y .- x)
@constraint(model, t .>= x .- y)
@objective(model, Min, sum(t))
```
But JuMP actually has special support for this with the NormOneCone:
> **[Standard form · JuMP](https://jump.dev/JuMP.jl/stable/moi/reference/standard_form/#MathOptInterface.NormOneCone)**
>
> Documentation for JuMP.
```julia
# To model: sum(abs.(y .- x))
@variable(model, t)
@constraint(model, [t; y .- x] in MOI.NormOneCone(1 + length(x)))
@objective(model, Min, t)
```