How to express this optimization problem in CVX?

1

The optimization problem is described below:

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I wrote the following code, but it doesn’t seem to be correct. I hope someone can help me, I will be very grateful!

    clc,clear;
    %%========================Initialization parameter
    T=400;%Total flight duration
    N=T/0.5;%The flight time slot
    D=3*0.5;%Maximum flight distance
    H=100;%altitude
    P=-5;%The initial power
    Ppeak=4*P;%Maximum power value
    r0=80;%SNR
    Lambda=100;%A coefficient in a power expression
    v=10^(-4);%The convergence accuracy                                  
    %++++++Initializes the coordinate value
    xf=100;%UAV terminal coordinates
    yf=-600;
    x0=100;%UAV origin coordinates
    y0=600;
    xe=200;%Eavesdropper coordinates
    ye=0;
    xg=0;%Legitimate coordinates
    yg=0;
    %++++++Initialization variable
    xfea=100;
    yfea=600;
    ufea=580000;



    %%======================Use the CVX toolbox to find x, y
    for k=1:N

    cvx_begin 
        variables x(1,N) y(1,N) u(1,N) t(1,N);
        
    %++++++Compute the concave function f
         f=0;
         for i=1:N
             g=-P*u(1,i)/(log(2)*(ufea^2+P*ufea));
             h=-(rel_entr(t(1,i),t(1,i)+P)+rel_entr(t(1,i)+P,t(1,i)))/log(2);
             f=g+h+f;
         end
         
         maximize(f);
         
         subject to
         
         %+++++++C1
         for n=1:N
             t(1,n)+xfea^2-2*xfea*x(1,n)+2*xe*x(1,n)-xe^2+yfea^2-2*yfea*y(1,n) ...
                 +2*ye*y(1,n)-ye^2-H^2<=0;
         end
        
           %++++++++C2
             (x(1,1)-x0)^2+(y(1,1)-y0)^2<=D^2;
               for m=1:N-1
                    (x(1,m+1)-x(1,m))^2+(y(1,m+1)-y(1,m))^2<=D^2;
               end
             (xf-x(1,N))^2+(yf-y(1,N))^2<=D^2;
        
       %++++++++C3
         for n=1:N
            x(1,n)^2-2*xg*x(1,n)+xg^2+y(1,n)^2-2*yg*y(1,n)+yg^2+H^2-u(1,n)<=0;
         
        %++++++++C4
            t(1,n)>=H^2;
         end
         
         cvx_end
        
        fprintf('%f %f %f %f\n',x(1,k),y(1,k),u(1,k),t(1,k));
        xfea=x(1,k);
        yfea=y(1,k);
        ufea=u(1,k);
    end

It keeps displaying the following information after running. I don’t know why

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2

What is the output from cvx_version ? if using CVX 3.0beta, please switch to CVX 2.1.

Does the program make it through the first time through cvx_begin ... cvx_end ? If so, is the result that the problem is solved? Is it infeasible? Why is there for k=1:N loop outside cvx_begin .. cvx_end ?

I changed the outside for loop to for k=1:1 and the program ran to completion, declaring the problem to be infeasible. Please read https://yalmip.github.io/debugginginfeasible/ . I haven’t actually looked at your model or implementation, and have no idea if it is correct.

Perhaps you should start with a smaller version of the problem and get that working correctly before going to the full-size version.

3

Thank you very much for your answer. I don’t think my program is due to the CVX version. And I’m sure there’s nothing wrong with my model. In fact, I edited another executable program, but the result wasn’t what I wanted. Maybe I need to modify some of the initial values of the program to get the results I want. Nevertheless, I am very grateful for your reply.

4

Search this forum for narginchk and you will see why I asked you to show the output of cvx_version .

5

ok

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6

With regard to the narginchk error, I suggest you reinstall CVX, and look carefully for any errors or warnings during installation.

7

OK，thank you for your reply.
I 've solved the problem,and I reinstall a new version MATLAB,from MATLAB 2016a to MATLAB 2018b,the warning never come back.

8

What is your output in MATLAB 2018 ? I am using 2020 and there’s some error and results are NaN for all the variables. Is it correct ?
It is displaying your problem is infeasible.

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9

Perhaps you can show your program, complete with all input data.

The output you show says that the problem is infeasible. Hence the CVX variables have value NaN after CVX completes. Such values will cause an “invalid” error if then used in a CVX expression.

10

I just want to test the feasibility of the above code, and then write my own simulation program through this question and answer, but I found that the same error message appeared with you, my MATLAB version is 2020A, who can help me错误信息 , tell me why this situation occurs, and have you solved this problem? Thank you

11

The diagnosis is the same as what is in my post immediately preceding yours.