How can I model min-max problem

回答済み

Shawn Xu

2023年08月18日 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

  2023年08月18日 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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