problem: variables n: 18846055, constraints m: 56379024
cones: z: primal zero / dual free vars: 37612021
l: linear vars: 2
s: psd vars: 18767001, ssize: 1nnz(A): 58322374
This is a very large PSD problem. As you can see, this one solves in 4e4 seconds, so I assume it’s about the limit of what you can solve in a reasonable amount of time.
As a general rule of thumb, I tend to think of problems with <10^4 variables as easy, 10^5 as getting a bit hard, 10^6 as hard, and 10^7 as very hard. 10^8 as nigh impossible.
Why is the problem so large? What are you modeling? Have you looked at ways to simplify the problem?