# 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).

23 questions
Filter by
Sorted by
Tagged with
1 vote
85 views

### 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*} ...
483 views

### Maximize the minimal distance between true variables in a list

I'm using the OR-Tools CP-SAT solver on a list of $n$ boolean variables $x_i$. I'm trying to maximize the minimal distance between two true variables in this list, as illustrated by the following ...
165 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 $\theta$}} + \...
188 views

119 views

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 ...
122 views

### 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}\\ \...
250 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 ...
2k views

### 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 ...
799 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 ...