I already got a nice answer for a similar question (https://math.stackexchange.com/q/3734505) while now i am looking for a lower bound for the square root of the sum of variables including squares and binary decision variables to address a MILP with CPLEX:
Let's say we have some known parameters : $x_i > 0$ where and a set of binary decision variables $y_i \in \{0,1\}$ where i $\in [1,...,n]$
I am looking for a good lower bound of this term (a sum or something similar but not a one square root term):
$\sqrt{\sum_{i}y_ix_i^2}$
The constraint is written as follows by the way : $a - b \le z\sqrt{\sum_{i}y_ix_i^2}$ where $a$ and $b$ are positive decision variables and $z$ is a parameter ($z < 0$).
PS: $\min{x_i}$ is a lower bound but not of a good quality.