I want to know if such an expression is invalid

1

微信截图_20240429193720
微信截图_202404291937201900×654 73.1 KB

only x is a variable
I wrote the code as follows

cvx_clear
cvx_begin 
cvx_solver mosek
variable X(M,1)
variable eta
variable z
maximize eta
subject to 
% variable I_m(1,N)    
I_m = cvx(zeros(1,N));         
R = cvx(zeros(1));
for m=1:M
    R = R+b(m)*(log2(H_ST_m(m))+X(m)*log2(exp(1)))-c(m);
    R1 = cvx(zeros(1));  
    for m1 =1:M
        if Interfering_users(m,m1)>0
            {X(Interfering_users(m,m1)),1,z} == exponential(1);
            R1 = R1+z;
        end
    end
    R = R-b(m)*(-rel_entr(1,(R1*H_ST_m(m)+Im(m)+B*n0)))*1.44;
end
eta<=R;
for n = 1:N
    for k=1:K
        for m=1:M                    
            I_m(1,n) = I_m(1,n) + X_out(m,k)*P(m,1)*X_PU(n,k)*g_BS_m(m,n);
        end
    end
    I_m(1,n) <= In; % C1
end
for m=1:M
    {X(m),1,0} == exponential(1);
end
cvx_end

The current error is as follows
Disciplined convex programming error:
Invalid constraint: {real affine} <= {convex}

出错 <= (第 21 行)
b = newcnstr( evalin( ‘caller’, ‘cvx_problem’, ‘’ ), x, y, ‘<=’ );

出错 untitled (第 37 行)
eta<=R;
I’d appreciate it if I got help

2

I haven’t tried to decipher exactly what you are doing, but it seems like your code doesn’t match the problem in the image.

The 2nd term of R_{m,k} can be handled with log_sum_exp. The other exponentials in the problem can be handled directly with exp, without explicitly setting exponential cone constraints.

C3 isn’t directly allowed in CVX, but seems to be unnecessary, because it should be satisfied bu virtue of exp(...) being nonnegative.

3

Thank you very much
But for the 2nd term of Rm,k ,only a few of the variables x are included.So,how use log_sum_exp to handle it.

4

log(a+f1*exp(x1)+f2*exp(x2)) = log_sum_exp([log(a);x1+log(f1);x2+log(f2)];)

Use the correct indexing, and extend this to all the terms inside the log. And divide log_sum_exp by log(2) because of the log2 rather than log. I leave you to attend to those details.

5

Thank you very much
Unfortunately, however,I met other errors
Calling Mosek 9.1.9: 92 variables, 31 equality constraints
For improved efficiency, Mosek is solving the dual problem.

Status: Error
Optimal value (cvx_optval): NaN

无法将类型为 struct 的值用作索引。

出错 cvxprob/solve (第 429 行)
[ x, status, tprec, iters, y ] = shim.solve( At, b, c, cones, quiet, prec, solv.settings, eargs{:} );

出错 cvx_end (第 88 行)
solve( prob );

出错 untitled (第 47 行)
cvx_end
I tried not to use mosek ,but I met the same error

6

I restarted matlab. This problem has been successfully resolved. Thanks again