How to solve this problem: {convex} .* {convex},

I don’t know how to solve this problem, please help me, thank you very much.

variable W(ST,d,L) complex
variable x(K) 
variable y(K) 
expressions constant constraint_1(K) s_k b_k ...
constraint_2(K) constraint_3(K) ;

constant =norm([wx;(trans_maxpower_-1)/2],'fro'); 

c= 2*(trace(J1(:,:,1)*W(:,:,1)+J1(:,:,2)*W(:,:,2)));

for k=1:K
   for l=1:L
      s_k(:,k)=Gama_mini-(1+miu_bs)*norm( vec( G_k(:,:,k)' ),'fro' ).^2* norm( w(:,l),'fro' ).*norm( w(:,l),'fro' );  
   constraint_1(k)=-(G_sk_error(k)^2+N*D_n_error(k)^2 )*P*( 1+miu_bs  )*( norm( w(:,1) ).^2 +norm( w(:,2) ).^2 ) -2*sqrt( log(1/prob) ) *(x(k)+y(k)) +s_k(:,k); %37c ( (1+miu_bs)*trace(W*(W)') )
   constraint_2(k)=( 1+miu_bs  )*( norm( w(:,1) ).^2 +norm( w(:,2) ).^2 )*sqrt(G_sk_error(k)^2 +N*N*D_n_error(k)^2 ) * norm(G_k(:,:,k)',2)-sqrt(2) * x(k); %-sqrt(2) * x(k) 37d
   b_k=(sqrt( log(1/prob) ) +sqrt( log(1/prob) +2 ) )*0.5; %37f
   constraint_3(k)=b_k*(G_sk_error(k)^2 +N*D_n_error(k)^2 )*P* ( 1+miu_bs  )*( norm( w(:,1) ).^2 +norm( w(:,2) ).^2 )-y(k); %37e   sum_abs(W,L)*j

minimize  real(c)
subject to


J0 == hermitian_semidefinite(ST);

错误使用 .*
Disciplined convex programming error:
Cannot perform the operation: {convex} .* {convex}

出错 main (第 131 行)
s_k(:,k)=Gama_mini-(1+miu_bs)norm( vec( G_k(:,:,k)’ ),‘fro’ ).^2 norm( w(:,l),‘fro’ ).*norm( w(:,l),‘fro’ );

norm(x)^2 can be entered into CVC as square_pos(norm(x))

However, norm(x)*norm(y) is not allowed by CVX, and is not convex in general.

I will assume the problem is not convex. But if it is, it is your responsibility to prove it.

Hello, there is a new problem. I’m not sure which part is convex and which part is concave. Can you help me? I need your help urgently. thank you!

constraint_1(k)=-(G_sk_error(k)^2+N*D_n_error(k)^2 )*P*( 1+miu_bs  )*( square_pos(norm( w(:,1) ) ) +square_pos(norm( w(:,2) ) ) )-2*sqrt( log(1/prob) ) *(x(k)+y(k)) +s_k(:,k); 

错误使用 +
Disciplined convex programming error:
Illegal operation: {concave} + {convex}

出错 main (第 131 行)
constraint_1(k)=-(G_sk_error(k)^2+ND_n_error(k)^2 )P( 1+miu_bs )( square_pos(norm( w(:,1) ) ) +square_pos(norm( w(:,2) ) ) )-2*sqrt( log(1/prob) ) *(x(k)+y(k)) +s_k(:,k);

Did you read the link?

Yes, I did. But I don’t know how to solve it. :pensive:

Have you proven your problem is convex? That’s what the links says to do.

if the problem is not convex, CVX is not the right tool to use.

Well, thank you very much. Thank you