Model Definition

Answered

Francisco Mansilla

August 02, 2023 11:09

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Hello, I am blocked on how to model the following function.

 

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  Jaromił Najman

  • Gurobi Staff

  August 02, 2023 15:30

  Hi Francisco,

  Gurobi currently does not support the function \(x^y\) where both \(x\) and \(y\) are optimization variables. Thus, if \(z\) in your formulation is an optimization variable, then you cannot formulate \(f\) in Gurobi.

  Since you defined \(f(x)\) and not \(f(x,y,z\) I will assume that both \(y\) and \(z\) are constants. If \(z\) is an integer constant you can formulate your model as a quadratic one via additional auxiliary variables as described in How do I model multilinear terms in Gurobi? For example, if \(z=3\), you could formulate your model as

  \[\begin{align*}
  w_1 &= x -y\\
  w_2 &= w_1 \cdot w_1\\
  w_3 &= w_2 \cdot w_1\\
  w_4 &= x \cdot w_3
  \end{align*}\]

  If \(z\) is not integer, you could use the addGenConstrPow method. For example, if \(z=1.3\), you could formulate your model as

  \[\begin{align*}
  w_1 &= x - y\\
  w_2 &= w_1^{1.3} \quad (*)\\
  w_3 &= x \cdot w_2
  \end{align*}\]

  The \((*)\) constraint is implemented via

  model.addGenConstrPow(w_1, w_2, 1.3)

  Best regards, 
  Jaromił

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