How to solve ''Unable to perform assignment because value of type 'cvx' is not convertible to 'double'

1

Here I got this code and error message, could you please help me to solve it?

`cvx_begin
variable E_user(n) nonnegative
variable sigma(n) nonnegative
variable Sigma(n) nonnegative
variable Omega(n) nonnegative
obj=0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        sigma=zeros(1,K_num); Sigma=zeros(1,K_num); Omega=zeros(1,K_num);
    
        % Calculate sigma
        for t=1:K_num
            my_hold=zeros(M*N,M*N);
            for i=1:K_num
                if i~=t
                    my_hold=my_hold+E_user(i)*G_DDMA(:,:,i)*G_DDMA(:,:,i)';
                end
            end
            sigma(t)=trace(pinv(D(:,:,t))*U(:,:,t)*H(:,:,t)*my_hold*H(:,:,t)'*U(:,:,t)'*(pinv(D(:,:,t)))');
        end
    
        % Calculate Sigma
        for t=2:K_num
            my_hold=zeros(M*N,M*N);
            for i=2:K_num
                if i~=t
                    my_hold=my_hold+E_user(i)*G_DDMA(:,:,i)*G_DDMA(:,:,i)';
                end
            end
            Sigma(t)=trace(pinv(D(:,:,1))*U(:,:,1)*H(:,:,1)*my_hold*H(:,:,1)'*U(:,:,1)'*(pinv(D(:,:,1)))');
        end
        my_hold=zeros(M*N,M*N);
        for i=3:K_num
            my_hold=my_hold+E_user(i)*G_DDMA(:,:,i)*G_DDMA(:,:,i)';
        end
        Sigma(1)=trace(pinv(D(:,:,2))*U(:,:,2)*H(:,:,2)*my_hold*H(:,:,2)'*U(:,:,2)'*(pinv(D(:,:,2)))');
    
    
        % Calculate Omega
        for i=2:K_num
            Omega(i)=trace(pinv(D(:,:,1))*U(:,:,1)*H(:,:,1)*G_DDMA(:,:,i)*G_DDMA(:,:,i)'*H(:,:,1)'*U(:,:,1)'*(pinv(D(:,:,1)))');
        end
        Omega(1)=trace(pinv(D(:,:,2))*U(:,:,2)*H(:,:,2)*G_DDMA(:,:,1)*G_DDMA(:,:,1)'*H(:,:,2)'*U(:,:,2)'*(pinv(D(:,:,2)))');
    
        sigma=real(sigma);
        Sigma=real(Sigma);
        Omega=real(Omega);
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        for i=2:n
            obj=obj+log(1+2*beta(i)*sqrt(E_user(1)+alpha*Sigma(1)+N0)-beta(i)^2)*(N0+alpha*sigma(i)*Omega(1))/log(2);
        end
        obj=obj+log(1+2*beta(1)*sqrt(E_user(2)+alpha*Sigma(2)+N0)-beta(1)^2)*(N0+alpha*sigma(1)*Omega(2))/log(2);
        maximize (obj)
        E_sum=0;
        for i=1:n
            E_sum=E_sum+E_user(i);
        end
        subject to 
        E_sum<=E_total;
    cvx_end`

The error was ‘Unable to perform assignment because value of type ‘cvx’ is not convertible to ‘double’.’ in the line of ‘sigma(t)’

2

You seem to be confusing variable with expressions.

sigma=zeros(1,K_num); supersedes (overwrites) the earlier declaration of sigma as a variable. my_hold is a CVX expression, because it involves the variable E_user.The, sigma(t) is tassigned to a CVX expression involving my_hold, but sigma is a double, not a CVX expression; so triggers the error message.

You should declare

expression sigma(n) 
expression Sigma(n) 
expression Omega(n)

instead of as variables. Declared expressions are automatically initialized to all zeros by CVX. If you need them to be nonnegative, you will need to add the constraints

sigma >= 0
Sigma >= 0
Omega >= 0

Read:
CVX Users’ Guide: Assignment and expression holders

3

Thank you so much for your answer!

After I correct the expression error, I still got another error in the line to calculate the ‘obj’ within a for loop

cvx_begin
            variable E_user(n) nonnegative
            expression sigma(n) 
            expression Sigma(n) 
            expression Omega(n) 
            obj=0;
            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
         
%             sigma=zeros(1,K_num); Sigma=zeros(1,K_num); Omega=zeros(1,K_num);
        
            % Calculate sigma
            for t=1:K_num
                my_hold=zeros(M*N,M*N);
                for i=1:K_num
                    if i~=t
                        my_hold=my_hold+E_user(i)*G_DDMA(:,:,i)*G_DDMA(:,:,i)';
                    end
                end
                sigma(t)=trace(pinv(D(:,:,t))*U(:,:,t)*H(:,:,t)*my_hold*H(:,:,t)'*U(:,:,t)'*(pinv(D(:,:,t)))');
            end
        
            % Calculate Sigma
            for t=2:K_num
                my_hold=zeros(M*N,M*N);
                for i=2:K_num
                    if i~=t
                        my_hold=my_hold+E_user(i)*G_DDMA(:,:,i)*G_DDMA(:,:,i)';
                    end
                end
                Sigma(t)=trace(pinv(D(:,:,1))*U(:,:,1)*H(:,:,1)*my_hold*H(:,:,1)'*U(:,:,1)'*(pinv(D(:,:,1)))');
            end
            my_hold=zeros(M*N,M*N);
            for i=3:K_num
                my_hold=my_hold+E_user(i)*G_DDMA(:,:,i)*G_DDMA(:,:,i)';
            end
            Sigma(1)=trace(pinv(D(:,:,2))*U(:,:,2)*H(:,:,2)*my_hold*H(:,:,2)'*U(:,:,2)'*(pinv(D(:,:,2)))');
        
        
            % Calculate Omega
            for i=2:K_num
                Omega(i)=trace(pinv(D(:,:,1))*U(:,:,1)*H(:,:,1)*G_DDMA(:,:,i)*G_DDMA(:,:,i)'*H(:,:,1)'*U(:,:,1)'*(pinv(D(:,:,1)))');
            end
            Omega(1)=trace(pinv(D(:,:,2))*U(:,:,2)*H(:,:,2)*G_DDMA(:,:,1)*G_DDMA(:,:,1)'*H(:,:,2)'*U(:,:,2)'*(pinv(D(:,:,2)))');
        
            sigma=real(sigma);
            Sigma=real(Sigma);
            Omega=real(Omega);
            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            for i=2:n
                obj=obj+log(1+2*beta(i)*sqrt(E_user(1)+alpha*Sigma(1)+N0)-beta(i)^2)*(N0+alpha*sigma(i)*Omega(1))/log(2);
            end
            obj=obj+log(1+2*beta(1)*sqrt(E_user(2)+alpha*Sigma(2)+N0)-beta(1)^2)*(N0+alpha*sigma(1)*Omega(2))/log(2);
            maximize (obj)
            E_sum=0;
            for i=1:n
                E_sum=E_sum+E_user(i);
            end
            subject to 
            E_sum<=E_total;
        cvx_end
4

The error is ‘Disciplined convex programming error:
Cannot perform the operation: {concave} .* {real affine}’

Does this mean my objective is becoming a concave problem which can not be solved, where the cvx code are all fine.

5

You are violating CVX’s rules. Your first task is to prove that your optimization problem is a convex optimization problem. if it is, a reformulation to satisfy CVX’s DCP rules might be possible. If it is not a convex optimization problem, such a reformulation is not possible.

6

Ok, make sense. Thank you so much for your time and patience!