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I have a system with $C$ machine and $U$ users. The decision variables are $d_{u,c}$ and ${\bf f}_{u,c}$ with $c=1,2,\cdots,C$ and $u=1,2,\cdots,U$, where

$$d_{u,c}\in\{0,1\}$$ $${\bf f}_{u,c}\in\mathbb{C}^{N\times 1}\hspace{3mm}\text{(a vector of }N\text{ complex elements)}$$

I want to put a constraint like this:

If $d_{u,c}=0$, then $||{\bf f}_{u,c}||^2=0$

If $d_{u,c}=1$, then $0<||{\bf f}_{u,c}||^2\le T$

Here, $||\cdot||$ is Euclidean norm and $T>0$

How to model this constraints mathematically?

KGM
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1 Answers1

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$d_{u,c}\sigma \le ||{\bf f}_{u,c}||^2\le Td_{u,c}$
where $\sigma$ is a very small number based on scale of $f$

Sutanu Majumdar
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