I have an expression as following
\gamma_u=\frac{\sum_{c=1}^C\alpha_{u,c}P_c\sigma_{u,c}d_{u,c}^{-3.76}}{\beta+\sum_{c=1}^C(P_c\sigma_{u,c}d_{u,c}^{-3.76}-\alpha_{u,c}P_c\sigma_{u,c}d_{u,c}^{-3.76})}
and the constraint is as follows
\gamma_u \ge \gamma_{th},\forall u
Here, \alpha_{u,c} is a binary variable and 0\le P_c\le Pmax is a continuous variable.
We have multiplication of binary variable and continuous variables both in numerator and denominator in the form of \alpha_{u,c}P_c.
We can introduce auxiliary variable z_{u,c}=\alpha_{u,c}P_c and introduce these following constraints
\alpha_{u,c}p_l \le z_{u,c} \le \alpha_{u,c}p_u
P_c - p_l(1-\alpha_{u,c}) \le z_{u,c} \le P_c + p_u(1-\alpha_{u,c})
where p_u and p_l are upper and lower bound for P_c. Is this linearisation correct?
Also, how can I express the numerator, denominator expressions and the constraint?