How can I model min-max problem

Answered

Shawn Xu

August 18, 2023 14:25

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I am trying to minimize the max value of 'unov1' to find the worst case scenario. 'unov' is the multiplication of decision variables. Can I use

m.addGenConstrMax(unov1,[unov],name = "max over+under")

m.setObjectiveN(unov1)

to model the worst case scenario?

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  Maliheh Aramon

  • Gurobi Staff

  August 18, 2023 19:44

  Hi Shawn, 

  Yes, to model the optimization problem \(\min \max_i x_i\), you can model the \(\max\) constraint using the Gurobi APIs for general constraints. You can also model this problem as below (Gurobi would do exactly the same under the hood if you use general constraint APIs).

  \[\begin{align} \min z  & & \notag \\ \mbox{s.t.}~~ & z \geq x_i, ~~ \forall i & \notag \end{align}\]

  Best regards,

  Maliheh

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