Questions tagged [indicator-constraints]
For questions on constraints controlled by binary variables.
18
questions
1
vote
2answers
136 views
Switching of decision variables to be larger than or equal to a decision variable according to an indicator variable value
I would like to seek some advice on modeling the following:
I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is greater than or equal to a ...
4
votes
1answer
100 views
Switching of decision variables to be equal to a certain decision variable according to a binary (indicator) variable
I would like to seek some advice on modeling the following:
I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is to be equated to a third ...
1
vote
1answer
46 views
Formulating indicator constraint set
I am having difficulty formulating the indicator constraints for the following:
Consider a set of $A_{n}$ decision variables such that $A_{1},A_{2},⋯,A_{n}<A$. While all of them are integers that ...
2
votes
1answer
47 views
Reformulating to locate the second largest decision variable of a set of decision variables
Consider a set of $A_{vn}$ decision variables such that $A_{v1},A_{v2},\cdots,A_{vn}<A$. While this is the standard formulation finding the maximum value of $A_{vn}$, I would also like to find the ...
2
votes
1answer
98 views
Linearize sum of continuous and boolean variable
For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $ A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants ...
3
votes
2answers
115 views
Formulating the conditional constraint
I want to develop a model extension of capacitated location problem.
The variables are a binary $x_i$ and a continuous $Q_i$. The following condition must be satisfied:
if $x_i = 0$, $Q_i$ must be ...
3
votes
2answers
91 views
Model “If, then” constraint
How to model the following "If, then" type constraint?
If $\sum\limits_{i \in I}x_i = 0$ then $\sum\limits_{j \in J}x_{j} = n$
where $x$ are binary variables, $n$ is a known parameter and $...
4
votes
2answers
107 views
Faster implementation of “or” constraints in ILP
I have implemented a set of "or" constraints in my ILP using binary decision variables (as in this method). It works fine for smaller problems, but when I try to increase the number of ...
4
votes
1answer
203 views
Indicator function in math programming
I have the following doubt:
Being $x$ an integer variable that takes the values $1$, $2$ or $3$.
Being $y_1$ a binary variable.
Being $y_2$ a binary variable.
I want to express the two following ...
1
vote
0answers
45 views
linearisation of if-then constraint [duplicate]
Is it possible to translate this if-then constraint in linear manner to be solved with a linear programming solver?
If not, how can it be translated into a integer programming manner to be solved by ...
3
votes
1answer
108 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 ...
4
votes
1answer
94 views
How are indicator constraints implemented? [duplicate]
I wonder how systems like CPLEX, GUROBI, etc implement indicator constraints. Do they just implement Big M equivalents? If yes, what is then the justification for using them?
Edit
The question does ...
4
votes
2answers
285 views
How to convert this if-then constraint to MIP constraint?
How to convert this if-then constraint to MIP constraint?
$\text{if } a \geq 0 \text{ then } b=K_1 \text{ else(a <0 ) } \ b =K_2$
3
votes
1answer
99 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 ...
3
votes
1answer
98 views
How to fomulate the following conditional constraint in MILP?
How can I formulate the following conditional constraint to a linear constraint using indicator variables? Please note that all variables are continuous and $c \ge 0$
$\text{1: if} \ c=0 \ \& \ ...
3
votes
2answers
218 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 ...
11
votes
1answer
338 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\...
16
votes
5answers
2k views
When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs
Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model ...
