minimax optimization
AnsweredHello,
How can I solve the multiobjective problem?
F= min ( P *x + max (Q*x ) )
where x is the decision variable, and P and Q are constants.

Hi,
Are you sure that you want to solve a multiobjective problem? Because then your model should rather be something like
\[\begin{align*}
&\min (Px, Qx) \\
&\text{s.t. some constraints}
\end{align*}\]If you indeed want to solve a multiobjective model, please refer to our Documentation of Working with Multiple Objectives.
The formulation you wrote looks more like bilevel optimization. There is plently of literature on how to solve (mixedinteger) linear bilevel optimization problems. Most of them require the dualization of the second level. One good overview is provided by BenAyed 1993.
Best regards,
Jaromił0
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