Failed in sloving a convex probelm

1

My formulated problem is a convex optimization, but I failed in solving it with CVX. I will show my MATLAB CVX program, result and the problem below.

%% CVX-begin
zvq = zeros(q_num,1);
cvx_begin
variable x(3, node_num, q_num) nonnegative;
variable y(q_num, node_num, node_num, 2) nonnegative;  %2 means fi=[1,2,3], 3 will be instead by 2+1
variable p(uav_num, node_num) nonnegative;
variable b(uav_num, node_num) nonnegative;
variable z(q_num) nonnegative;
expression c0(node_num);
expression xx(3);
maximize  (rqi*z- ALPHA_P*sum(sum(p)))
subject to
x<=1;
y<=2;
z<=1;
for qi = 1:q_num
    x(1, sd(qi,1), qi)==z(qi); % constrain-1
    x(3, sd(qi,2), qi)==z(qi); % constrain-2
    for n = 1:node_num
        for fi = 1:2
            sum(y(qi,n,:,fi))-sum(y(qi,:,n,fi)) == x(fi, n, qi)-x(fi+1, n, qi);
        end
        
        if qi==1 % c0 is sums of each node for constarin-7
            c0(n) = cqi(qi,:)*x(:,n,qi);
        else
            c0(n) = cqi(qi,:)*x(:,n,qi) +c0(n);
        end
    end
    sum(x(:,:,qi),1)<=1; % constrain-5
    sum(x(:,:,qi),2)>=z(qi);
    %             sum(sum(x(:,:,qi)))*delta_tq(qi,:)'<=tqi(qi); % constrain-6
end
c0<=cn'; % constrain 7
sum(p,2) <= pmax';% constrain-9 (None 8)
%% maybe bug1 ?
for n = 1:bs_num
    for m = 1:node_num
        if m<=bs_num
            sum(y(:,n,m,:),4)'*lq<=lg1; % constrain-11-a
        else
            sum(y(:,n,m,:),4)'*lq<=lg2/3;% constrain-11-b
        end
    end
end
%% maybe bug2 ?
for n = 1:uav_num
    for m = 1:node_num
        for fi = 1:2
            y(:,n+4,m,fi)'*lq<=-rel_entr(b(n,m), b(n,m) + p(n,m)*H(n,m)/cigma)/log(2); % constrain-12   x*f(y/x) = -rel_entr(x,x+y)
        end
    end
end
sum(sum(b))<=B; % constrain-13
cvx_end

end

CVX Warning:
Models involving “rel_entr” or other functions in the log, exp, and entropy
family are solved using an experimental successive approximation method.
This method is slower and less reliable than the method CVX employs for
other models. Please see the section of the user’s guide entitled
The successive approximation method
for more details about the approach, and for instructions on how to
suppress this warning message in the future.

Successive approximation method to be employed.
** For improved efficiency, SDPT3 is solving the dual problem.**
** SDPT3 will be called several times to refine the solution.**
** Original size: 6849 variables, 3034 equality constraints**
** 42 exponentials add 336 variables, 210 equality constraints**
-----------------------------------------------------------------
** Cones | Errors |**
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
** 0/ 36 | 8.000e+00 2.963e+04 2.963e+04 | Failed**
** 0/ 36 | 8.000e+00 2.726e+04 2.726e+04 | Failed**
** 0/ 36 | 8.000e+00 2.650e+04 2.649e+04 | Failed**
-----------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaN

2

This is my problme formulation :hot_face:

11
11882×736 17.6 KB

3

and when I remove the constrain-12, it will be solved

4

If you have access to Mosek (9,x), use that as solver, under CVX 2.2 Otherwise follow the advice at 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

5

Thank you sincerely！ And I will try in this way!

6

If it doesn’t work, see Handling numerical issues section of

7

Thank you! I’ve tried to solve my problem by Mosek and it works successfully. Only one little problem exists. I’ll read this page later.