Please excuse the dumb question, but I am totally lost, as I have never seen a sum notation like this before. I am no mathematician, so please excuse me if this is somehow trivial.
I am currently looking at implementing a mathematical model. x is a binary variable.Given indices i, j, $\alpha$ and $\omega$, where $\alpha$ and $\omega$ are indices for the same set, but with different names, D is one set, U is a number and V the number of elements in $\alpha$ and $\omega$, is somebody able to tell me what this expression means?
$$ \sum_{i \in D} \sum_{U \leq \alpha \leq \omega \leq V} x_{i,j,\alpha, \omega} $$
I know that $$ \sum_{\alpha, \omega} = \sum_{\alpha} \sum_{\omega} = \sum_{\omega} \sum_{\alpha} $$ but i am not able to figure out what the expression above means... I would be very thankful for your help!
$$\sum_{i \in D}\sum_{U\leq \alpha\leq \omega \leq V}f(i,\alpha,\omega)$$ $$=\sum_{i \in D}\sum_{\alpha=U}^{V}\sum_{\omega=\alpha}^{V}f(i,\alpha,\omega)$$