Linked Questions
13 questions linked to/from In an integer program, how can I “activate” a constraint only if a decision variable has a certain value?
4
votes
0answers
89 views
Conditional constraint formulation [duplicate]
How can I create constraints to make sure $x=1$ if $k\geq 0$ and $x=0$ if $k<0$, where $x\in \{0,1\}$ and $k\in \mathbb{R}$?
Here is my attempt:
\begin{equation}\label{cons:1}
\begin{aligned}
...
23
votes
3answers
4k views
In an integer program, how I can force a binary variable to equal 1 if some condition holds?
Suppose we have a binary or continuous variable $x$, a binary variable $y$, and a constant $b$, and we want to enforce a relationship like
If $x \gtreqless b$, then $y = 1$.
How can we write this ...
12
votes
4answers
726 views
Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?
Is there a single crisp and accessible reference which covers how to generate Mixed Integer Programming formulations to linearize products, handle logical constraints and disjunctive constraints, do ...
12
votes
1answer
1k views
If-then constraints in MIP programming
For continuous variables $x$ and $y$, the constraints are:
...
4
votes
2answers
170 views
Conditional Constraint in MIP
I need to formulate a conditional constraint for a binary variable z defined as:
$z_{i,j,k}$, $\ \ i=1:10 \ , \ j=1:5 \ , \ k=1:3$
If any $z_{i,j,3} = 1$ then $z_{i,j,1} + z_{i,j,2} = 0 \ \ \...
12
votes
1answer
445 views
Representing an indicator function: binary variables and “indicator constraints”
I want to represent the indicator function:
$$ \mathbb{1}_{(y=j)}$$
where $y$ is a non negative, integer variable.
My attempt is as follows: define a binary variable:
$$ z_j =\begin{cases}
1 \qquad\...
3
votes
2answers
286 views
Mocking up conditional statements in LP
I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically:
1. Is it ...
3
votes
1answer
119 views
Linearizing constraint with continuous and boolean variables
I have two continuous variables $A$, $B$ and two binary variables $x$, $y$.
Condition: if $A = B \wedge x = 1 \wedge y=1$ then $z = 1$ else $z = 0$ from
In an integer program, how I can force a ...
2
votes
1answer
77 views
Same values constraint and grouping of variables
In a linear program, I would like some variables to:
1. Take the same values
2. Group some variables i.e. some variables should take same values or lie within certain percentage.
3. All different ...
3
votes
1answer
107 views
How to transform these conditional constraints to linear integer ones in a more efficient way?
The conditional constraints A and B can be transformed to a set of linear integer constraints as follows:
A) $\text{if} \ x_1=0 \ \text{then} \ d_1=1 \ \text{else} \ d_1= 0\\ x_1\in {\rm I\!R}^{\geq ...
5
votes
1answer
64 views
How to formulate case distinctions in AMPLs objective function?
This is my first real optimisation problem I formulated and now trying to solve by using AMPL.
The following objective function is from a linear 0-1 LP means all variables $x_i^b\in\{0,1\}$, with $i\...
3
votes
1answer
115 views
How to optimize with “if” constraints
The minimizing problem is the following :
$$ \underset{w}{\operatorname{argmin}} \sum_{i=1}^{n}\left[w_{i}\times (\frac{Vw}{\sigma})_{i} - b_{i}\right]^{2}$$
with $V$ a $n\times n$ matrix (covariance ...
1
vote
1answer
58 views
How to model this chain of logical implication
I would like to seek some advice on modeling the following (chain of) logical implication:
For instance $\omega_{xy}$ might indicate precedence, i.e., $x$, $y$ being the nodes $x$ and $y$, ...