Why the sqrt({convex}) is wrong?

1

I don’t know why it is wrong when I use sqrt({convex}).

There are my codes:

Hmax=500;
H=zeros(1,Omax);
H(:,o)=(0.2*Hmax);
tempRate=zeros(48,1);
while 1
cvx_begin
        variable Hopt(1,Omax)
        expression tempRate(48,1)
        expression f
        for i=1:length(q)
            a=q(i,:);
            for j=1:U
                re2(j+(i-1)*U)=sum((a-w(j)).^2 ,2);
            end
        end
        re=re2';  
        **d=sqrt(Hopt(1,o)^2+re);**

This is my equation:
image

image

2

Use norm because sqrt(convex) is not allowed in CVX.

d=norm([Hopt(1,o),sqrt(re)]);

You might be able to do what you want with norm(suitable vector) without using all those for loops, but I’m not clear on the dimensions or everything, so I’ll leave those details to you.

help cvx/sqrt
Discipined convex programming information for sqrt:
sqrt(X) is log-concave and nondecreasing in X. Therefore, when used
in DCPs, X must be concave (or affine).

Disciplined geometric programming information for sqrt:
   sqrt(X) is log-log-affine and nondecreasing in X. Therefore, when
   used in DGPs, X may be log-affine, log-convex, or log-concave.
3

Thank you very much for your help! I am trying it.

4

I try to use this method to solve the following problems：
QQ截图20230302163333
QQ截图20230302163401
but the following errors：

QQ截图20230302163701
QQ截图202303021637011046×208 8.01 KB

what can I do to solve it?

5

I’m not sure this is right. So I leave you to check this and fix it up.
sqrt(w'*b*(U*x*x'*U'+eye(N))*w = (sqrt(b)*x'*U'*w)'*(sqrt(b)*x'*U'*w) + w'*w) = norm([sqrt(b)*x'*U'*w;w])

it it can be done, I believe you will need to do this or sometthing similar, using norm.

6

OK，that is solved.Thanks! Mark