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).

Filter by
Sorted by
Tagged with
4
votes
1answer
92 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: $$...
1
vote
0answers
34 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 ...
2
votes
0answers
81 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}\\ \...
4
votes
0answers
193 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 ...
3
votes
2answers
509 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
votes
1answer
115 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 ...
-4
votes
1answer
71 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)...
5
votes
1answer
114 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 ...
2
votes
1answer
252 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 ...
2
votes
1answer
784 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 ...
33
votes
4answers
850 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 ...
17
votes
1answer
2k 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 ...