PWL objective function

Answered

Wei-Ting Tang

October 01, 2023 03:20

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I want to minimize (f1(x1)*f2(x2))

 

where f1 and f2 are both represented by piecewise linear function.

How can I model this objective function in gurobi?

Related to

• Piecewise Linear

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  Jaromił Najman

  • Gurobi Staff

  October 02, 2023 13:22 Edited

  You can model the following equivalent formulation

  \[\begin{align*}
  \min &\,\,z_1 \cdot z_2 \\
  z_1 & = f_{1}^{pwl}(x_1) \,\, (1)\\
  z_2 & = f_{2}^{pwl}(x_2) \,\, (2)
  \end{align*}\]

  You can use the addGenConstrPWL() method to model the equalities \((1)\) and \((2)\). Note that you will have to introduce 2 auxiliary variables \(z_1, z_2\). Since Gurobi supports bilinear terms, you can then multiply the two in the objective function.

  Best regards, 
  Jaromił

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