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
1
vote
1
answer
88
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*}
...
- 205
3
votes
0
answers
176
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 $\theta$}} + \...
- 4,010
2
votes
3
answers
191
views
Is there any "not bad" algorithm that can solve the minimax problem in 0/1 integer programming?
As title, recently I got a minimax problem, after formalizing, the model is like this.
$$\text{minimise } \max_{k \in K} \sum_{i \in I} b_{i,k} \cdot f_i$$
such that: $$ \forall i \in I,\, \sum_{k \in ...
- 23
2
votes
1
answer
113
views
Correct way to set a quadratic constraint Xpress
I'm implementing on Xpress a problem with different solution proposed on a paper. The idea is to decompose a matrix $X$ into a convex sum $\sum_{t}\lambda_t M^{(t)}$, where each $M^{(t)}$ has only ...
- 123
5
votes
3
answers
484
views
Maximize the minimal distance between true variables in a list
I'm using the OR-Tools CP-SAT solver on a list of $n$ boolean variables $x_i$. I'm trying to maximize the minimal distance between two true variables in this list, as illustrated by the following ...
- 235
1
vote
0
answers
32
views
How to create distinct groups in LP?
Say you have the following table:
Season Crop Price
Spring
Cauliflower
175g
Spring
Coffee
15g
Summer
Blueberry
50g
Fall
Beet
100g
Fall
Eggplant
60g
I want to choose the best selling crop for ...
- 11
2
votes
1
answer
93
views
How do we call this optimization problem?
Let $f_k\colon\Bbb R^n\to\Bbb R$, $k=1,\dots,K$, be differentiable (possibly nonconvex) functions and $X\subset\Bbb R^n$ be a convex set.
Consider the following optimization problem:
$$
\min_{x\in X}\...
- 155
1
vote
0
answers
152
views
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
5
votes
1
answer
852
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 ...
- 61
2
votes
0
answers
318
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 ...
- 21
4
votes
1
answer
120
views
Convex-Constrained Nonconvex-Nonconcave Minimax Problem
In the mathematical optimization theory, I have taken a glance at many papers which deal with the unconstrained convex-concave or nonconvex-concave minimax optimization, i.e.,
$$
\min_{x\in X}\ \max_{...
- 155
4
votes
1
answer
177
views
Continuous minimax with linear objective and constraints
How to solve the following minimax problem quickly? The variables are all continuous.
$$\max_{x_{1}, x_{4}, x_{5}} \min_{x_2,x_3} \vec{c}^{\intercal} \vec{x}$$
subject to the following constraints:
$$...
- 523
1
vote
0
answers
116
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
2
votes
0
answers
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}\\
\...
- 523
4
votes
0
answers
253
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 ...
- 523