Hey!

I’m currently working on solving the following problem. Here I use successive convex aproximation of the function 1/mu in constraint (1c).

Until now, the problem in CVX only converges if I use Mosek at default (not best) precision. Is there a reason why solvers like sedumi or sdpt3 are not converging?

I tried to simulate the problem from this post which also uses exponential sets, and it worked with all solvers.

Thanks in advance,

Markus K

```
clear;
close all;
% === Simulation constant parameter ===
K = 2; % Number of ground user
delta = 40*1e-3; % Time slot duration [s]
V_max = 70; % Maximum velocity [m/s]
A_0 = db2pow(-30); % [dB]
sigma_n = sqrt(db2pow(-90) * 1e-3); % [dB]
kappa_m = 1e6;
B = 1e06 ; % Bandwidth [Hz]
E_min = db2pow(0); % Minimum energy level fronthaul channel [dB]
P_kmax = ones(1, K) * db2pow(23) * 1e-3; % Maximum power for each user [dB]
D = 0.5 * 1e06; % Amount of data [bit]
Q_max = (K + 1) * 100 * D; % Maximum buffer capacity [bit]
sigma = 1;
theta_channel = rand(K, 1) * 2*pi;
h_k = sqrt(kappa_m /(kappa_m + 1)) * sigma .* exp(1i * theta_channel) ...
+ sqrt(1/(kappa_m + 1)) * randn(1, 1, "like", 1i) .* sigma;
% === Simulation location parameter ===
height_uav = 100;
GU_pos = randn(2,K);
GU_pos = [25, 25; 15, 5; 0, 0];
beta_k = [1; 1];
% === Local parameter for simulation ===
iter_max = 30;
mu_k_sca_last = ones(2, 1);
for iter_sca = 1: iter_max
% === CVX - Problem ===
cvx_begin
cvx_solver sedumi;
% cvx_solver sdpt3;
% cvx_solver mosek;
cvx_precision low
% Optimization variables
variable u_pos(2, 1) nonnegative %
variable r_k(K, 1) nonnegative % Channel capacity (fronthaul channel)
variable b_k(K, 1) nonnegative % Bandwidth of the channel (fronthaul channel)
variable mu_k(K, 1) nonnegative % Slack variables
variable z_k(K, 1) nonnegative
variable x nonnegative;
maximize(x)
% == Constraints ==
subject to
% C3a -
z_k <= mu_k+ b_k;
for k = 1:K
% => Version with exponential set {(x, y, z) | y > 0, y*exp(x/y) <= z }
% b_k .* exp((r_k .* log(2))./b_k) <= z_k
{r_k(k) * log(2), b_k(k), z_k(k)} == exponential(1);
% => Version with relative entropy {rel_entr(x, y) = x*log(x/y)}
% r_k(k) * log(2) + rel_entr(b_k(k), z_k(k)) <= 0;
% C3b -
GU_num = 2;
C_k = sigma_n^2/(A_0 * abs(h_k(k))^2);
C_k * pow_pos(norm([u_pos; height_uav] - GU_pos(:, k)), 2) - P_kmax(k)*(2/mu_k_sca_last(k) - mu_k(k)/mu_k_sca_last(k)^2) <= 0;
end
% C4 - total bandwidth for all channels
sum(b_k(:)) <= B;
% C5 - mimumum SNR ???
r_k >= b_k * E_min;
% C8 - data volume
r_k .* delta >= beta_k .* x;
cvx_end
% === update SCA ===
mu_k_sca_last = mu_k;
end
```