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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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:...
5 votes
1 answer
497 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
161 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
89 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_{...
  • 133
4 votes
1 answer
127 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
0 answers
60 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 ...
  • 111
2 votes
0 answers
102 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
0 answers
212 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
2 answers
1k 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
1 answer
387 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
95 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
126 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
1 answer
571 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
2k 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
990 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
1 answer
3k 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 ...