The problem of constraint expression with norm in CVX

1

Dear Professor, I would like to ask you a question about CVX. The procedure is as follows：

a=rand(66,33);
A=rand(66,6);
x_1_0=rand(6,1);
x_2_0=rand(6,1);
B=rand(66,30);
G=rand(60,30);
The constraints of CVX are as follows：
norm(a'*(A*x_1_0+B*β_1-A*x_2_0-B*β_2)-5*sqrt(3))
In which β_1=norm((M_1*G+v_1),1),β_2=norm((M_2*G+v_2),1),
M_1,v_1,M_2,v_2 are variables in CVX, defined as follows:
     variable M_1(30,60);
     variable v_1(30,1);
     variable M_2(30,60);
     variable v_2(30,1);

I don’t know how to express the second-order norm constraint including the first-order norm in CVX. I hope you can help me,thanks

2

Have you proven this i s convex?

3

If β_1 is convex, the constrain is connvex

4

Please show us the proof.

5

Actually, I didn’t prove it, but I did program it to define β as a variable, not a first order norm, and it would run.i do not know it’s different

6

norm is not affine, so can’t be used in an argument of norm.

help cvx/norm

Disciplined convex programming information:
norm is convex, except when P<1, so an error will result if
these non-convex “norms” are used within CVX expressions. norm
is nonmonotonic, so its input must be affine.

Please carefully read

7

What can be used to replace the first order norm? Can the Max function be used

8

You apparently have either not read or have not understood the link.