Linear programming: Condition on index variable

Question

Let $i \in \{1,2,...n\}$. And let $X_i \in \{0,1\}$.

I need to write the condition: if all $X_i$ where $i$ is even index take the value 1, then there need to be at least three $X_i$ with value $0$ for all $i$'s with odd index.

The problem I am having is that I cannot put this into one equation if the condition does not hold.

It is obviously that is will not work if I type this: $\sum_{i = even}X_i \geq \sum_{i = odd}X_i + 3$, because if the upper condition does not hold, that the above equation need not to be fulfilled.

score 0 · Answer 1 · answered May 15 '15 at 17:52

0

Regarding the condition on even terms as a boolean should work, like this:

$$\left(\prod_{i\: even}X_i\right)\left(\sum X_i\right)\le n-3$$

answered May 15 '15 at 17:52

Joffan

39,627

What about $\sum X_i \leq n -3(\prod_{i : even} X_i)$ – Zenga May 15 '15 at 19:34
That works too, I guess. I'm not saying mine is the only way. – Joffan May 15 '15 at 19:46

Linear programming: Condition on index variable

1 Answers1