Array of constraints Julia

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I am trying to get an array of constraints, but I keep getting different kinds of errors, and I don't know what I'm doing wrong.

data array is 77x9 (integer values)

foods is a column vector of size 77x1, a variable of array type

lower is a column vector of 9x1, an integer vector

I should have 9 constraints

Here is what I have,

model2 = Model()
@variable(model2, foods[i=1:77] >= 0)  # Quantity of food

 for i ∈ 1:9
 for j ∈ 1:77
 @constraint(model2, c2[i], sum(data[j][i]*foods[j])<=lower[i])
 end 
 end
julia-jump ijulia-notebook julia mathematical-optimization optimization
1 Answers

What you want to do is

@constraint(model2, data' * foods .<= lower)

Explanation

Let's make a toy example:

julia> @variable(model2, foods[i=1:3] >= 0)
3-element Vector{VariableRef}:
 foods[1]
 foods[2]
 foods[3]

julia> data = collect(reshape(1:12, 3, 4))
3×4 Matrix{Int64}:
 1  4  7  10
 2  5  8  11
 3  6  9  12

julia> lower = rand(101:104, 4)
4-element Vector{Int64}:
 104
 102
 102
 102

For such case you can use just matrix multiplication:

julia> data' * foods
4-element Vector{AffExpr}:
 foods[1] + 2 foods[2] + 3 foods[3]
 4 foods[1] + 5 foods[2] + 6 foods[3]
 7 foods[1] + 8 foods[2] + 9 foods[3]
 10 foods[1] + 11 foods[2] + 12 foods[3]

Now adding the right hand side constraint (note that we vectorized the <= operator:

julia> @constraint(model2, data' * foods .<= lower)
4-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.LessThan{Float64}}, ScalarShape}}:
 foods[1] + 2 foods[2] + 3 foods[3] <= 104.0
 4 foods[1] + 5 foods[2] + 6 foods[3] <= 102.0
 7 foods[1] + 8 foods[2] + 9 foods[3] <= 102.0
 10 foods[1] + 11 foods[2] + 12 foods[3] <= 102.0
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