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).
22
questions
3
votes
0
answers
77
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 $\theta$}} + \...
- 3,980
2
votes
3
answers
157
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: $$ \forall i \in I,\, \sum_{k \in ...
- 23
2
votes
1
answer
110
views
Correct way to set a quadratic constraint Xpress
I'm implementing on Xpress a problem with different solution proposed on a paper. The idea is to decompose a matrix $X$ into a convex sum $\sum_{t}\lambda_t M^{(t)}$, where each $M^{(t)}$ has only ...
- 123
5
votes
3
answers
461
views
Maximize the minimal distance between true variables in a list
I'm using the OR-Tools CP-SAT solver on a list of $n$ boolean variables $x_i$. I'm trying to maximize the minimal distance between two true variables in this list, as illustrated by the following ...
- 235
1
vote
0
answers
32
views
How to create distinct groups in LP?
Say you have the following table:
Season Crop Price
Spring
Cauliflower
175g
Spring
Coffee
15g
Summer
Blueberry
50g
Fall
Beet
100g
Fall
Eggplant
60g
I want to choose the best selling crop for ...
- 11
2
votes
1
answer
91
views
How do we call this optimization problem?
Let $f_k\colon\Bbb R^n\to\Bbb R$, $k=1,\dots,K$, be differentiable (possibly nonconvex) functions and $X\subset\Bbb R^n$ be a convex set.
Consider the following optimization problem:
$$
\min_{x\in X}\...
- 155
1
vote
0
answers
141
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
777
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
291
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
116
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.,
$$
\min_{x\in X}\ \max_{...
- 155
4
votes
1
answer
166
views
Continuous minimax with linear objective and constraints
How to solve the following minimax problem quickly? The variables are all continuous.
$$\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
104
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
119
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
241
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
3
votes
2
answers
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
...
- 2,211
2
votes
1
answer
733
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
...
- 205
-4
votes
1
answer
187
views
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)...
- 235
5
votes
1
answer
154
views
Minimize binary variable's distance with respect to the index values
For a given binary decision variable $x[i,j,k]$ my goal is to get as dense results in terms of k for successive values of j. Distance of k value to be kept as close as possible throughout j values:
$d ...
- 315
2
votes
1
answer
759
views
Defining and comparing utilization rates for delivery service
I'm currently working on a case for a food delivery service and wondered whether my notion of "driver utilization" makes any sense.
My data set contains an hourly overview of the
number of active ...
- 23
2
votes
1
answer
3k
views
how to implement a constraint with max/min function in pyomo
I am implementing a NLP problem in pyomo, and I am getting some issues for this constraint:
\begin{equation}
\forall i \in \lbrace 1, N \rbrace , \forall j \in \left\{1, M \right\}: Y_{i,j} \cdot ...
- 534
33
votes
4
answers
1k
views
Why are integer minimax problems hard?
Problems that have a minimax-type structure are notoriously hard to solve. For example, the $p$-median problem from facility location (choose $p$ facilities to minimize demand-weighted distance to ...
- 13.1k
17
votes
1
answer
5k
views
The difference between max-min and min-max
I am solving two-stage optimization problems in the form of
$$\max_{x \in X}\min_{y \in Y} f(x,y),$$
where $f(x,y)$ is the solution of a mixed integer linear program (MIP). As the constraints of the ...
- 1,859