How to express the norm^2 in cvx?

1

I want toe express the following expression in the cvx, i.e.,
norm(conj(transpose(v))Hw)^2

where ‘v’ is a complex variable of size K*1, ‘H’ and ‘w’ are all given variables.

In the code, I expressed the above expression as ‘pow_p(norm(conj(transpose(v))Hw),2)’.

But the cvx gave warning as follows:

Disciplined convex programming error:
Illegal operation: pow_p( {convex}, {2} )

2

square_pos(norm(...))
or
pow_pos(norm(...),2)

As can be seem below, when the 2nd argument of pow_p is 2, the first argument of pow_p must be affine, which norm is not.
help pow_p

pow_p Positive branch of the power function.
pow_p(X,P) computes a convex or concave branch of the power function:
P < 0: pow_p(X,P) = X.^P if X > 0, +Inf otherwise
0 <= P < 1: pow_p(X,P) = X.^P if X >= 0, -Inf otherwise
1 <= P : pow_p(X,P) = X.^P if X >= 0, +Inf otherwise
Both P and X must be real.

Disciplined convex programming information:
    The geometry of pow_p(X,P) depends on the precise value of P,
    which must be a real constant:
             P < 0: convex  and nonincreasing; X must be concave.
        0 <= P < 1: concave and nondecreasing; X must be concave.
        1 <= P    : convex  and nonmonotonic;  X must be affine.
    In all cases, X must be real.
4

HAHA!
Initially, I just find the pow_p and do not find the pow_pos.

Sir! Thank you very much! Thanks for your help!
I have asked many questions in this forum! And you help me a lot! :grinning: :grinning:

5

You should (re-)read this section of the CV User’s GUide http://cvxr.com/cvx/doc/funcref.html# , for a list of all the functions, and some other stuff.

help <function name> has more information than the CVX Uses’ Guide. For instance, whether arguments need to be affine, convex, or concave.