Invalid constraint: {complex affine} >= {convex},how do i rewrite the code of formula,which has two variables

1

123456789

I am going to write the code about this formula,but it has some problems,hoping someone can teach me how to modify it.My problem code will begin the %========my problem of code begin here===========

%OP4
%declare
K=4;
N=4;
L=5;%distance between RX & TX
nois_var_hk_2pow=0.1*(L^(-2.5))
nois_var_ak_2pow=[10^-7 10^-7 10^-7 10^-7 ];
nois_var_dk_2pow=[10^-5 10^-5 10^-5 10^-5 ];
bar_r=[10 10 10 10];
P_T=10000;
h_1=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_2=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_3=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_4=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_kk=cat(2,h_1 ,h_2 ,h_3, h_4)
 for n=1:4
    h_k{n}=h_kk(1:4 , n);
    n=n+1;
 end


cvx_begin

    variable FNNK(N,N,K) semidefinite;%c7
    variable rho_k(1,1,K) semidefinite;
    variable P

Fkk=cat(2,FNNK);
    
    u=0
   for o=1:4
       Fk{o}=Fkk(1:4,o+3*u:4*o)
       u=u+1;
   end
 %===============my problem of code begin here================
   c5_left_hand = 0;
    for k = 1:K
        sumja = 0;
        for j = 1:K
            if j ~= k  
             sumja = sumja +  h_k{k}' * Fk{j} * h_k{k};
            end
         end
       c5_left_hand = c5_left_hand - sumja+ (h_k{k}' * Fk{k} * h_k{k}*inv_pos(bar_r(1)))
    end
    
  c5_right_hand= nois_var_ak_2pow(1)+ ( nois_var_dk_2pow(1)*inv_pos(rho_k(k)) )

   c5_left_hand >=  c5_right_hand

And the window told me

Error using cvxprob/newcnstr (line 192)
Disciplined convex programming error:
   Invalid constraint: {complex affine} >= {convex}

Error in  >=  (line 21)
b = newcnstr( evalin( 'caller', 'cvx_problem', '[]' ), x, y, '>=' );

Error in op4 (line 74)
       c5_left_hand >=  c5_right_hand

How do i rewrite the code of formula ?if i modify to real(c5_left_hand) >= real( c5_right_hand),the error will become

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


Error in  *  (line 36)
    z = feval( oper, x, y );

Error in op4 (line 89)
            c10_left_hand = c10_left_hand + rho_k(k)*sumja10+nois_var_ak_2pow(1);
2

Because h_k has complex cell elements, there are roundoiff level imaginary components in the summands comprising c5_left_hand. Using real(c5_left_hand) eliminates the imaginary component, thereby allowing
real(c5_left_hand) >= c5_right_hand
So you have already resolved that difficulty.

As for your error

Error in op4 (line 89)
c10_left_hand = c10_left_hand + rho_k(k)*sumja10+nois_var_ak_2pow(1);

You haven;t shown us the code which comes before it. What is sumja10.? If it is a CVX expression, as is sumja, then you have a multiplication of two CVX variables, which is non-convex, and could produce the error message you received. I don’t see anything in the image you posted which looks like it would correspond to such code.

3

i just want to write a for loop for it,so i will set sumja=0 in the begining,just like

a=0
for b=1:10 
   a=a+b
end

so the code means a=0 first,then a =0+1=1,then a=1+2=3,and so on

4

What does that code have to do with your error message? Your ''b was apparently the “illegal” multiplication of two CVX expressions (or variables, not a non-CVX number.

5

you means i multiply two cvx variables so the window show me the error? I have seen this error and modification in your other answer ,so i have modified it before.the variable in this code are just Fk{k} and rho_k

And in the both c5_left_hand and c5_right_hand,there are no multiplication of two cvx variables

6

To be honest, i don’t understand this error meaning

7

AS I wrote previously
real(c5_left_hand) >= c5_right_hand
is accepted by CVV and does not produce any error messages.

You need to show your complete code if you want someone to figure out what your remaining errors are.

8

modify as you said,the code is ok,but as I wrote previously ,if i write the as real(c5_left_hand) >= real(c5_right_hand),why there is a error like below,but real(c5_left_hand) >= c5_right_hand is ok.

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


Error in  *  (line 36)
    z = feval( oper, x, y );

Error in op4 (line 89)
            c10_left_hand = c10_left_hand + rho_k(k)*sumja10+nois_var_ak_2pow(1);
9

You STILL have not shown the preceding code. You have not shown us how sumja10 is determined. If, as appears to be the case, sumja10 is a CVX expression, there is an “illegal” multiplication of CVX variables or expressions, hence the error message.

10 
hat_p_lb=-59.2081
%OP4
%declare
K=4;
N=4;
L=5;
nois_var_hk_2pow=0.1*(L^(-2.5))
nois_var_ak_2pow=[10^-7 10^-7 10^-7 10^-7 ];
nois_var_dk_2pow=[10^-5 10^-5 10^-5 10^-5 ];
bar_r=[10 10 10 10];
%P_hat=0.00001;
P_T=10000;
h_1=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_2=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_3=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_4=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_kk=cat(2,h_1 ,h_2 ,h_3, h_4)
 for n=1:4
    h_k{n}=h_kk(1:4 , n);
    n=n+1;
 end


cvx_begin

    variable FNNK(N,N,K) semidefinite;%c7
    variable rho_k(1,1,K) semidefinite;
    variable P
%==========================
Fkk=cat(2,FNNK);
    
    u=0
   for o=1:4
       Fk{o}=Fkk(1:4,o+3*u:4*o)
       u=u+1;
   end
   tr_ace=0
   for t=1:K
       tr_ace=tr_ace+trace(Fk{t})  
   end
%====================================    
%object function
    minimize( tr_ace )
%==================================== 
%Constraint 
subject to 
%c3
rho_k<=1

%c5
%===================================================
       c5_left_hand = 0;
        for k = 1:K
            sumja = 0;
            for j = 1:K
                if j ~= k  
                 sumja = sumja +  h_k{k}' * Fk{j} * h_k{k};
                end
            end
           
            c5_left_hand = c5_left_hand - sumja+ (h_k{k}' * Fk{k} * h_k{k}*inv_pos(bar_r(1)))
        
        end
        

      c5_right_hand= nois_var_ak_2pow(1)+ ( nois_var_dk_2pow(1)*inv_pos(rho_k(k)) ) 
       real( c5_left_hand ) >=   c5_right_hand
%===================================================   
%c10
    c10_left_hand = 0;
        for k = 1:K
            sumja10 = 0;
            for j = 1:K
                if j ~= k  
                 sumja10 = sumja10 +  h_k{k}' * Fk{j} * h_k{k};
                end
            end
            c10_left_hand = c10_left_hand + sumja10+nois_var_ak_2pow(1);
        end     
        for k=1:K
   c10_right_hand=hat_p_lb*inv_pos(1-rho_k(k))
        end
       real(c10_left_hand)>= real( c10_right_hand)
cvx_end
11

i know your meaning now,i forget to paste the code about sumja10,here is the total code,and you can see the sumja10 just like the sumja,but sumja10 is in the constraint 10,sumja is in the constraint 5.Sorry for my mistake

now the problem about constraint 10 is

Error using cvxprob/newcnstr (line 192)
Disciplined convex programming error:
   Invalid constraint: {real affine} >= {concave}

Error in  >=  (line 21)
b = newcnstr( evalin( 'caller', 'cvx_problem', '[]' ), x, y, '>=' );

Error in op4 (line 96)
       real(c10_left_hand)>= real( c10_right_hand)
12

You haven;t shown the code for hat_p_lb, therefore the problem us not reproducible. However, given the error message you received, which shows that c10_right_hand is concave, it must be that hat_p_lb < 0 when the error message was produced,.because inv_pos(1-rho_k(k)) is convex.

Also note that every time through the for loop from 1 to K, c10_right_hand is being overwrittten, so its value when used in the following constraint is hat_p_lb*inv_pos(1-rho_k(K)) and the first K-1 times through the for loop have no effect on the optimization problem, i.e., are meaningless.

13

hat_p_lb is a negative value,so you mean that it has to be a positive value,or the error will be shown?
rho_k(k) is not all the same value,that’s why i still write it in the for k=1:K loop,i mean,the rho_k(1) is not equal to rho_k(2),etc. i said rho_k(k) ,not rho_k(K)

14

A negative number times a convex expression is a concave expression, It is not allowed to have concave_expression <= anything or anything >= concave_expression. I.e.,such a constraint is non-convex.

The last time through the for loop, k has the value K, so that is the only one used, because
c10_right_hand is overwritten every time through the loop.

15

oh i know your meaning now,i think have to modify this code for a little bit

16

so if i want a negative number times something to be convex expression, that something has to be “concave expression”? can you should me how modify a convex expression to be concave expression?

17

so if i want a negative number times something to be convex expression, that something has to be “concave expression”?

Yes.

Ar this point, you don;t need help in CVX, you need help in the mathematics of convex optimizatio. I suggest you read and solve a lot of the exercises in at least the first 5 chapters of “Convex Optimization”, by Boyd and Vandenberghe, which is freely downloadable at Convex Optimization – Boyd and Vandenberghe . If you have difficulties getting through that book, https://math.stackexchange.com/ would be a more appropriate forum than this one to get assistance. You will never learn anything by taking problems you don’t understand from books and papers and trying to implement them in CVX.,