How to write log(1+Ax)? A are two constant

[jarry (junjie jiang)]

How to write log(1+Ax)? A are two constant.

[Erling (Erling D.Andersen)]

What is a two constant?

Why not just doing

t=1+A*x;
t >= 0.0
log(t)

[jarry (junjie jiang)]

sorry,A is a constant
cvx can’t identify log
i want to know how to Convert log(1+Ax) to rel_entr（。 ）

[jackfsuia (Jack)]

You do not need to convert log(1+Ax) to rel_entr since CVX can accept log as I remember.

[Erling (Erling D.Andersen)]

Post the error message you got. And maybe your complete code.

[jarry (junjie jiang)]

my error message is cvx can not deal with log ，i need help to convert it

[jarry (junjie jiang)]

I have try it,
CVX can not deal with log(1+X)
do you know how to deal with it?

[Michal_Adamaszek]

You must show a full example that produces your error please. Otherwise really nobody has an idea how to help you. For example this works:

cvx_begin
variable X
maximize log(1+X)
subject to
X <= 10
cvx_end

[jarry (junjie jiang)]

cvx_begin
% cvx_solver mosek
variables P(K,N)
maximize (sum( A(k,:).*log2(phi(k,:).*P(k,:)+L_int(k, ) ))

    subject to

    for k = 1:K
        delta*sum(A(k,:).*(L_int(k,:)+phi(k,:).*P(k,:))) >= data2(k);
    end

   for k = 1:K
      beta* delta*sum(  (L_int(k,:)-A(k,:))/SoD(k,:).*P(k,:) ) >= energy(k);
    end

    for k = 1:K
        for n = 1:N
            0 <= P(k,n) <=20;
        end
    end
    
    for n = 1:N
          
           P(1,n)== P(2,n) == P(3,n);
      end
cvx_end  

The function ‘log2’ corresponding to the input parameter of type ‘CVX’ is not defined.
I need help. I don’t know how to do it.

[jarry (junjie jiang)]

cvx_begin
% cvx_solver mosek
variables P(K,N)
maximize (sum( A(k,:).*log2(phi(k,:).*P(k,:)+L_int(k,: ) ) )

subject to

for k = 1:K
    delta*sum(A(k,:).*(L_int(k,:)+phi(k,:).*P(k,: ) )) >= data2(k);
end

for k = 1:K
beta* delta*sum( (L_int(k,:)-A(k,:))/SoD(k,:).*P(k, ) >= energy(k);
end

for k = 1:K
    for n = 1:N
        0 <= P(k,n) <=20;
    end
end

for n = 1:N
      
       P(1,n)== P(2,n) == P(3,n);
  end

cvx_end

The function ‘log2’ corresponding to the input parameter of type ‘CVX’ is not defined.
I need help. I don’t know how to do it.

[jackfsuia (Jack)]

log2(x)=log(x)/log(2), according to math.

[jarry (junjie jiang)]

Thanks, it works.
I am a newcomer to CVX
You have been a great help to me

[jarry (junjie jiang)]

I have encountered new problems, i need help.

[jackfsuia (Jack)]

I guess some elements of A(k, : ) are <= 0 but some are not. You can read the error that implied something like that. Maybe you can paste your complete code on here next time if convenient.

[jarry (junjie jiang)]

for K = 5

T = 70; N = 140; delta = T/N;

w = [50,150,200,450,475;
125,100,350,300,450];

for c = 1:K
    data(1,c) = 200;  % 初始化需要传输的数据量(bit)
end

 for c = 1:K
    data2(1,c) = 2^200;  % 初始化需要传输的数据量(bit)
end
for c = 1:K
    energy(1,c) = 0.0001;  % 初始化需要传输的数据量(bit)
end

for c = 1:2
    for n = 1:N
        Q_int(c,n) = 500/N*n;  % 初始化无人机路径
    end
end

for k = 1:K
for n = 1:N
L_int(k,n) =1; % 初始化无人机路径
end
end

for a = 1:K
    for n = 1:N
        P_int(a,n) = 4;  % 初始化发射功率
    end
end

N_0 = -100; H = 20; 

% 噪声功率（单位转换）

dBm = N_0 ;
sigma = power(10, dBm/10 ) /1000 ; % 单位 w

% Unit conversion of beta_0 
beta = 1000 ;

% variables
%T = 75; N = 140;  
delta = T/N; 


% the square of distance between UAV and kth GN in time slot n
for k = 1:K
    for n = 1:N
        d(k,n) =  norm( Q_int(:,n) - w(:,k) );
        SoD(k,n) = power( d(k,n), 2 ) + power(H,2);
        phi(k,n) = beta/sigma/SoD(k,n);              % 计算 phi_k[n]
        changshu1(k,n) = log2(L_int(k,n)+phi(k,n).*P_int(k,n))
        changshu2(k,n) = beta*P_int(k,n)/SoD(k,n)
    end
end 
    
     % 使用CVX工具包求解调度参数
cvx_begin

% cvx_solver mosek
variables A(K,N)
maximize (delta*sum( A(k,:).*changshu1(k, ))
subject to

    % constraint 21
    for k = 1:K
        delta*sum(  A(k,:).*changshu1(k,:) ) >= data(k);
    end
    
    for k = 1:K
        delta*sum( (L_int(k,:)-A(k,:)).*changshu2(k,:) ) >= energy(k);
    end

    %13 14
    for n = 1:N
     
        sum(A(:,n)) <= 1;
    end

    % 19 20
    for k = 1:K
        for n = 1:N
            A(k,n) >= 0;
            
        end
    end

cvx_end

E_1 = delta*sum( A(k,:).*changshu1(k, );

cvx_begin
% cvx_solver mosek
variables P(K,N)
maximize (delta*(sum( A(k,:).*(log(phi(k,:).P(k,:)+L_int(k,:)) -0.2(2^(sum(P(k,:))))))))
subject to

    % constraint 21
   for k = 1:K
      delta*(sum( A(k,:).*(log(phi(k,:).*P(k,:)+L_int(k,:))))) >=  data(k) ;
      
   end

    %13 14
   for k = 1:K
      beta* delta*sum(  (L_int(k,:)-A(k,:))/SoD(k,:).*P(k,:) ) >= energy(k);
    end
    % 19 20
    for k = 1:K
        for n = 1:N
          
            0 <= P(k,n) <=20;
        end
    end
    for n = 1:N
          
           P(1,n)== P(2,n) == P(3,n)== P(4,n) == P(5,n);
      end
cvx_end  

Thanks, you give me a great help.

[jarry (junjie jiang)]

I show my code,please check my code，thanks.

[jackfsuia (Jack)]

The output said it’s infeasible. Maybe it is infeasible.

[Erling (Erling D.Andersen)]

It seems you use cvxquad. I doubt that is needed and it is better to use Mosek without cvxquad as described in the 2020 update on:

CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions

How to use CVXQUAD’s better performing and more reliable Pade Approximant instead of CVX’s unreliable Successive Approximation method: Update as of the release of CVX 2.2 in January 2020: Except for use of Quantum (Matrix) Entropy and Matrix Logarithm related functions addressed later in this post, none of the following, to include reformulation, is necessary if CVX 2.2 is used with Mosek 9.x as solver, in which case CVX will utilize Mosek 9.x’s native exponential cone capability, thereby avoid…

[Mark_L_Stone]

The output shows that CVX’s Successive Approximation method was used with SDPT3 as solver. cvx_solver mosek is commented out.

But as @Erling wrote, it would be better to use Mosek (with CVX 2.2) thereby avoiding CVX’s Successive Approximation method, and getting a more robust and reliable solution.

As for infeasible problems, follow the advice, except for section 1, in https://yalmip.github.io/debugginginfeasible, which also applies to CVX.

[jarry (junjie jiang)]

I use MAC
I have been unable to install Mosek properly
I have an official license ，but i don’t know how to use it.
Do you have any experience in this field