# 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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### How to model $\max\limits_{x\in X} \min\limits_{y\in Y} \max\limits_{z\in Z} f(z)$ as single MILP

I have the following optimization problem: \begin{align*} \max\limits_{x\in X} &\min\limits_{y\in Y} \max\limits_{z\in Z} & f(z) \\ &\text{such that} & (x, y, z)\in P \end{align*} ...
167 views

### 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 $\theta$}} + \...
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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
849 views

### How to model a max-min-max problem?

Everyone knows how to model max-min or min-max problems. I have a problem with objective to maximize min-max. So it can be called as a max-min-max problem. Any ideas how to model it efficiently? The ...
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311 views

### 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 ...
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• 523
1 vote
114 views

### MLE application with gekko in python

I want to implement MLE (Maximum likelihood estimation) with gekko package in python. Suppose that we have a DataFrame that ...
• 127
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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
251 views

### 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 ...
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### How can I express this max-min in CPLEX?

Initially, I had the below objective function $\max \sum_{u=1}^{U}\sum_{c=1}^{C}x_{u,c}d_{u,c}$ where $x_{u,c}$ are optimization variables I modelled this in CPLEX as ...
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801 views

### How to determine least time required to complete all tasks?

I am trying to figure out how can I assign tasks to workers in a way that maximum time required to complete all tasks is minimum. Suppose I have following matrix ...
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### How to change a function from Min(F(x)) to -Max(-F(x))?

I have not a good knowledge in math field, I am working on multi objective functions, and I have two maximization functions, and one minimize function, where: Max (X,Y) = X+Y Max (L,M) = Sum (LC + MD)...
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