Getting error in this

1

Error using *
Disciplined convex programming error:
Invalid quadratic form: product is complex.

Error in Jan12_SumRate (line 138)
        2*real(((v_0*H_hat+H_Direct_WET(i,:))*a_k(:,i)).'*((v0*H_hat+H_Direct_WET(:,i))*ak(:,i))) -abs(((v_0*H_hat+H_Direct_WET(:,i))*a_k(:,i)))^2 >= b_k-(log(z(i)))/q_k;    
% v0 and ak optimal, used this for next iterations

I have checked the expression and it is correct as per my understanding. I am running for loop, i=1:K. and defined following variables in cvx

cvx_begin
    variable t(2) nonnegative;
    variable f(K) nonnegative;                  %tau_k=p_k*t1
    variable z(K) nonnegative;
    variable v_0(1,N1) complex;
    variable a_k(M,K) complex;Kindly help.

thank you.

2

CVX does not allow abs(...)^2.

However, you can use square_abs(...) instead.of abs(...)^2.

3

Still error persists.

Invalid quadratic form: product is complex.

4

Where else does your program have a multiplication of variables?

5 
cvx_begin
    variable t(2) nonnegative;
    variable f(K) nonnegative;                  %tau_k=p_k*t1
    variable z(K) nonnegative;
    variable v_0(1,N1) complex;
    variable a_k(M,K) complex;
    dual variables y4 y5 y6 y7 y8 y9 y10 y11 y12;
    % Objective function
    expression R_k(K)
    R_k(i)=-rel_entr(t(2,1),t(2,1)+sum(f(i)*Kappa(i)))/log(2);
maximize sum(R_k);
    % Constraints
    subject to
        % SCA based constraints
        **2*real(((v_0*H_hat+H_Direct_WET(i,:))*a_k(:,i)).'*((v0*H_hat+H_Direct_WET(:,i))*ak(:,i))) -square_abs(((v_0*H_hat+H_Direct_WET(:,i))*a_k(:,i))) >= b_k-(log(z(i)))/q_k;**   
        f(i)<=X_k*((t(1,1)/1+z(i))-((t(1,1)/(1+z(i))^2)*(zk(:,i)-z(i)))+(2*sqrt(t(1,1))/(1+z(i)))*(sqrt(t0)-sqrt(t(1,1))))-Y_k*t(1,1);
        % Time, Power constraint and positivity constraints
        y4 : t(1,1)+t(2,1) <= Tmax;
        y5 : t(1,1) >= 0;
        y6 : t(2,1)>= 0;
        y7 : sum(norm(a_k))<=Pmax;
        y8 : abs(v_0(N1))<=1;
        f(i)>= 0;
        z(i)>= 0;
cvx_end

This is my code, i running it inside a for loop i=1:K
the line which is bold is giving error.

6

((v_0*H_hat+H_Direct_WET(i,:))*a_k(:,i))
has multiplicatio0n of v_0 and a_k, both of which are variables. That should be sufficient to cause the error message. i don’t know how many other errors your program contains.

It would appear that you have not done SCA correctly, given that you have this non-convex item.