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

```
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