# Questions tagged [indicator-constraints]

For questions on constraints controlled by binary variables.

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### 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 ...
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### 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 ...
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### 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 ...
110 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 ...
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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 ...
341 views

### How to convert this if-then constraint to MIP constraint?

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