# 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 ...
• 193
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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 ...
• 1,249
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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....
• 30.5k
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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 ...
• 2,180
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### How to convert this if-then constraint to MIP constraint?

How to convert this if-then constraint to MIP constraint? $\text{if } a \geq 0 \text{ then } b=K_1 \text{ else(a <0 ) } \ b =K_2$
• 294
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 ...