How to express it by using CVX? It is a SOCP problem (Moderator note: it is not an SOCP)

Nonconvex
1

Hi, I want to use CVX to solve this problem:
image
The first and second constraints are SOCP constraints.
My Matlab codes are as follow:
cvx_begin
variable W(2Nt)
minimize norm(W)
subject to
norm([atW;theta]) <= abs(arW)sqrt(1/Tr);
norm([brW;theta])<=abs(btW)*sqrt(1/Tt);
cvx_end
But it is wrong.
I hope someone can help me.Thanks!

2

image

3

this is not even convex, so it can not be a socp.

4

Thanks for your reply. I’m new to CVX learning.
Constraint is equivalent to image
so I think it is a SOCP constraint.
If it is not a socp problem,how can I to express it?

5

if you can gurantee arw >= 0, then it is a socp. but generally, it is not. so it can’t be expressed with cvx. cvx only accept convex constraints.
see the following for further advice

6

Thanks for your help.I will think again。