Define Piecewise Function as a Constraint in Julia

Question

I have an optimization model to which I need to add the following piecewise function as a constraint:

C_{i,k} = { PR_{i} * HSE_{k} i∈Ω, k = 1,...,M,    
            1                i∈Ω, k = 1,...,M 

I read PR and HSE from excel cells

¿Is there a nice way to do this in Julia? I have not found any documentation on this in Julia

Answer 1

A piecewise linear function is something like:

  f(x) = a⋅x+b  for x <= p
         c⋅x+d  for x > p

There may be more segments.

You describe just an OR (not a piecewise linear function):

  C[i,k] = PR[i]⋅HSE[k]  OR 1

What you describe can be modeled with an extra binary variable δ[i,k] ∈ {0,1} as:

   C[i,k] = (PR[i]⋅HSE[k])⋅δ[i,k] + (1-δ[i,k])

This is linear, as PR and HSE are constants. I assume that C is a decision variable.