Error using .* (line 262) Disciplined convex programming error: Invalid quadratic form(s): not a square

Nonconvex
1

Thanks all.

question
question.jpg4032×3024 1.68 MB

The picture should be less than or equal to rouk’k
This is my question. Here I want to prove it is quasi-concave. So I expressed the denominator in the form of a norm, finally, I can prove that the function of the up-level set can be expressed as SOC.
But there was an error in cvx: Error using . (line 262) Disciplined convex programming error: Invalid quadratic form(s): not a square.*
Part of my code is

cvx_begin 
variable cauy(M,K)
variable rou(K,K)
%% -----------------------------calculate subject 2 left
X = zeros(K,K,M);
for k=1:K
    for ii=[1:k-1,k+1:K]
        for m=1:M
            X(ii,k,m) =( 4/pi*abs( ( BETAA(m,k) * sqrt(Gammaa(m,ii)) * cauy(m,ii) / BETAA(m,ii) ) * ( sum( BETAA(:,k) .* (Gammaa(:,ii).^0.5) .* cauy(:,ii) ./ BETAA(:,ii) ) - BETAA(m,k) * sqrt(Gammaa(m,ii)) * cauy(m,ii) / BETAA(m,ii) ) ) )^0.5;
        end
        sb5_left(ii,k) = norm( X(k,ii,**:**) );
    end
end
cvx_end

In my question, only cauy is a variable, and all of the arguments are greater than or equal to zero. I hope you can help me. Thank you

2

X(ii,k,m) is kind of a mess. It appears to violate multiple DCP rules. Even if it were DCP-compliant, it isn’t affine, and therefore taking its norm is not allowed. Please re-read Why isn't CVX accepting my model? READ THIS FIRST! and the CVX Users’ Guide.

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.

3

Dear Stone, thank you for your reply. Because of the variable’s product that appears in my expression, I violated CVX’s rules. But can you tell me how to change it in this situation? Thank you.

4

I am presuming this is non-convex unless someone shows otherwise.

5

I doubt CVX is going to be able to solve your problem, even if it is convex (and of that I remain skeptical)

6

thanks for your reply！