I met a challenging problem that is described in matlab code as:
cvx_begin
% cvx_quiet(true)
variable E_k1(K,N_tot)
variable E_k2(K,N_tot)
variable E_k3(K,N_tot)
variable t_k1(K,N_tot)
variable t_k2(K,N_tot)
variable t_k3(K,N_tot)
variable l_u(K,N_tot)
variable l_h(K,N_tot)
variable l_a(K,N_tot)
minimize sum(sum( E_k1 + E_k2 + E_k3 + 1^2pow_pos(l_u,3)+ 1^2pow_pos(l_h,3) ))
subject to
for n=1:N_tot
sum(l_h(:,1:n),2) <= sum(-B0*rel_entr(t_k1(:,1:n),t_k1(:,1:n)+gamma0_bar(:,1:n).*E_k1(:,1:n))/log(2)/1e6,2);
end
l_a <= -B0*rel_entr(t_k2,t_k2+gamma0_bar.*E_k2)/log(2)/1e6;
l_a <= -B0*rel_entr(t_k3,t_k3+gamma1_bar.*E_k3)/log(2)/1e6;
l_u + l_a + l_h >= L_kn_max_arr/1e6;
c_u*l_u <= 2;
c_h*l_h <= 1;
E_k1>=0; E_k1<=t_k1*10;
E_k2>=0; E_k2<=t_k2*10;
E_k3>=0; E_k3<=t_k3*31.62;
l_u>=0; l_h>=0; l_a>=0;
t_k1+t_k2+t_k3<=1;
t_k1>=0; t_k1<=1;
t_k2>=0; t_k2<=1;
t_k3>=0; t_k3<=1;
cvx_end
Where gamma0_bar and gamma1_bar are given constant value whithin (0,1), and B0=1e6. If the variable dimension is small, the problem is well solved. While the dimension of variable gets to KN_tot=330, the detailed result is displayed as follows:
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: 6435 variables, 2379 equality constraints
1209 exponentials add 9672 variables, 6045 equality constraints
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
595/595 | 1.003e+00 3.829e-02 4.386e-09 | Solved
476/477 | 8.000e+00 9.213e+00 1.658e-08 | Solved
523/526 | 8.000e+00 5.462e+01 1.745e-07 | Solved
192/209 | 8.000e+00 1.881e+01 2.009e-08 | Solved
103/141 | 8.000e+00 5.458e+01 1.267e-07 | Solved
154/182 | 8.000e+00 5.297e+01 6.979e-08 | Solved
124/157 | 8.000e+00 5.721e+01 2.896e-07 | Solved
107/138 | 8.000e+00 4.475e+01 1.535e-08 | Solved
78/126 | 8.000e+00 6.038e+01 4.203e-09 | Solved
68/ 99 | 8.000e+00 2.136e+02 3.165e-09 | Solved
40/105 | 8.000e+00 7.442e+05 4.437e-09 | Solved
57/100 | 8.000e+00 2.358e+05 1.862e-09 | Solved
126/132 | 8.000e+00 7.497e+04 1.086e-08 | Solved
88/118 | 8.000e+00 8.173e+06 2.332e-09 | Solved
66/ 70 | 8.000e+00 7.255e+06 3.941e-09 | Solved
55/ 92 | 8.000e+00 2.338e+06 1.043e-08 | Solved
73/105 | 8.000e+00 7.448e+05 8.597e-09 | Solved
49/ 74 | 8.000e+00 2.388e+05 4.619e-09 | Solved
42/ 83 | 8.000e+00 7.527e+04 2.465e-09 | Solved
22/ 52 | 8.000e+00 1.414e+06 4.914e-09 | Solved
21/ 55 | 8.000e+00 4.353e+05 4.422e-09 | Solved
16/ 49 | 8.000e+00 5.176e+04 8.864e-09 | Solved
18/ 60 | 8.000e+00 4.714e+05 7.975e-09 | Solved
34/ 81 | 8.000e+00 2.328e+06 5.535e-09 | Solved
66/ 98 | 8.000e+00 5.941e+06 1.894e-08 | Solved
Status: Failed
Optimal value (cvx_optval): NaN
I do not know why the optimal result cannot be obtained by CVX for a large demension although the processes show “Solved” status. I really hope someone can help me and give me some directions.
