The problem of constraint expression with norm in CVX

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

The constraints of CVX are as follows:
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

Have you proven this i s convex?

If β_1 is convex, the constrain is connvex

Please show us the proof.

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

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

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

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