Thanks for the reply. I got some new insights I wanted to share, which is why I removed the previous post.
Indeed, there is the warning on SeDuMi (this one: Installing CVX Version 2.2 Build 1148). Reinstalling CVX did not remove the warning. However, as suggested in that post, this is unlikely to cause any issue if SeDuMi is not used.
Changing solver to MOSEK did not solve the problem. After some more experiments, I noted that the presolve does terminate, only the time increases exponentially. Below is a simpler MWE.
If I increase the parameter m (i.e., the number of rows of matrices A1 and A2), the presolve time increases as follows:
m=100: time=0.2 sec
m=200: time=2.7 sec
m=400: time=12 sec
m=800: time=52 sec
m=1600: time=235 sec.
For any reasonably large problem with matrices A1,…,A50 and m around 2000 for each, this presolve step takes over 30min, whereas solving the model (using different implementations) takes 4 minutes.
clear
load('mwe_cvx_data'); %Load matrix A1 and A2
[m,n] = size(A1); %m=1600, n=600
cvx_begin
%Initialize variable x
variable x(n)
%Initialize objective variable y
variable y
%Initialize variable matrix d
variable d(m,2)
%Objective is epigraph of sum of exponentials (via log_sum_exp)
minimise(y);
subject to
d(:,1) == A1*x;
d(:,2) == A2*x;
log_sum_exp(-0.4*(d(:,2) - 40)) <= log(m*y); %epigraph constraint
d(:,1) <= 35.0;
x>=0;
cvx_end