How to model these constraints correctly

Question

$W$ is a vector of $N$ complex elements. $D$ is a binary variable

The requirements are: when $D==1$, $L_{\min}\le ||W||_2^2\le L_{\max}$ and when $D==0$, $||W||_2^2=0$

I have formulated the following constraints to fulfill the requirements

$||W||_2^2\ge 0$

$||W||_2^2\le L_{\max}$

$||W||_2^2\le DL_{\max}$

$||W||_2^2\ge DL_{\min}$

Using programming language

 norm(W)>= 0
 norm(W)<=sqrt(Lmax)
 norm(W)<=D*sqrt(Lmax)
 norm(W)>=D*sqrt(Lmin)

norm is a convex function. Is convex>=0 a valid model?

Have I modeled them correctly?

Answer 1

The first and second constraints can be omitted. The third and fourth constraints are sufficient, as you can see by considering both cases for $D$.