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I have a MILP formulation where one of the parameters in the constraints is unknown but comes from a know uncertainty set (Robust Optimization approach). As far as I researched the first step for formulating the robust counterpart is to identify the worst case of the realized uncertainty and either max/or min it.

What are the best ways to identifying the worst case that comes from the uncertainty set?

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  • $\begingroup$ What is the form of the uncertainty set? for the parameter? $\endgroup$ Feb 7, 2023 at 13:24

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Worst case implies either lower (max)/upper bound (min). I'd try using duality principle as feasible solution to the dual will give me a bound to the primal objective. So you can use the bounds of the random variable as a constraint, solve the dual, then use the value found for the random and the dual bound as constraints on the objective, re-solve.

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