Questions tagged [indicator-constraints]
For questions on constraints controlled by binary variables.
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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 ...
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If-then constraint with continuous variables
I was usually using if-then constraints with integer variables but ended up using continuous variables and got confused. I have variables $x_{ij}\in\mathbb{R}_{\geq 0}$, and would like to force the ...
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How to enforce logical implication $\sum_j a_j x_j \le b \implies \sum_j c_j x_j \le d$
Some modeling languages and solvers support indicator constraints of the form $$y=\hat{y} \implies \sum_j a_j x_j \le b,$$ where $y$ is a binary decision variable and $\hat{y}\in\{0,1\}$ is a constant....
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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 ...
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How to convert this if-then constraint to MIP constraint?
How to convert this if-then constraint to MIP constraint?
$\text{if } a \geq 0 \text{ then } b=K_1 \text{ else(a <0 ) } \ b =K_2$
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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 ...
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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 $...
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How to couple a binary variable to a continuous variable to indicate values greater 0
I have a continuous variable $x_t$. A binary variable $b_t$ should be coupled to $x_t$ such that $b_t$ has the value $1$ if $x_t$ has a value greater than $0$ and $b_t$ has the value $0$ if $x_t$ has ...
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