How to linearize this IF-THEN constraint?

MIDCP
1

I have a nonlinear constraint as below

If x_k=0, Then ||{\bf w}_k||==0

If x_k=1, Then ||{\bf w}_k||>0

Here,

x_k\in\{0,1\} is a binary variable and ||\bf x|| gives the norm of vector \bf x.

{\bf w}_k\in\mathbb{C}^{N\times 1} is also an optimization variable. It is a vector of complex elements.

How can I linearize this?

2

I see Johan has now solved this for you at https://math.stackexchange.com/questions/3174408/how-to-linearize-this-if-then-constraint .Johan knows what he’s doing.

3

Yes…The constraint now can be linearized!