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optimizationjuliaconstraintspiecewisejulia-jump

Define Piecewise Function as a Constraint in Julia

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

Solution

  • 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.