# Questions tagged [minimax]

For questions relating to optimization problems in which the goal is to minimize the maximum value of some function (or maximize the minimize the value).

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### Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
• 523
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### Changing the order of $\sup$ and $\inf$

I have a problem in the following form \begin{align} \begin{array}{cll} \sup_{\theta \in \mathrm{dom}(f)} & \inf_{z \in \mathbb{R}^n} & \underbrace{f(\theta)}_{\text{concave in $\theta$}} + \...
• 4,000
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### Solving minimax problems with Gurobi

I want to solve a problem of the form $\min_x\max_y f(x,y)$ using Gurobi, where $x,y\in [0,1]$. Is there a simple way to model this in Gurobi? I've seen examples where the domain of $y$ is finite, but ...
• 21
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### Minimax problem with a large high dimensional feasible region

How to solve minimax mixed integer problem with a large high dimensional feasible region? \begin{aligned} \max_{\vec{x}}\min_{\vec{y}} \quad & \vec{r} \cdot \vec{x} + \vec{s} \cdot \vec{y}\\ \...
• 523
1 vote
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### How to create distinct groups in LP?

Say you have the following table: Season Crop Price Spring Cauliflower 175g Spring Coffee 15g Summer Blueberry 50g Fall Beet 100g Fall Eggplant 60g I want to choose the best selling crop for ...
• 11
1 vote
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### Minimax MILP problem

I have a MILP model which defines a relation between three real variables $x$, $y$ and $s$ where $s = f(x,y)$. I want to optimize the following objective: $$\min_x\max_y s$$ How can I achieve it? EDIT:...
• 91
1 vote