I am looking to solve a class of SDPs with complex entries, with the semi-definite cone $S^n$, $n$ around 5000 to 15000. Also, $m$, the number of equality/inequality constraints is close to $n$.
CVX, but I quickly run out of memory for $n=1000, m=1000$ (I have about 50 GB available). Could you suggest other (free) SDP solvers that I could use?
I looked at the documentation for
SDPA, and it claims to have much lower memory usage than the solvers mentioned above. In one of the cases, the memory use is claimed to be around 5% as
SDPT3. The matrices in my problem aren't very sparse, but there are about 20% non-zeros.
SDPA is a good combination for my problem?
Please note that I have complex numbers involved, and I would like to avoid changing my formulation to convert everything into real, if possible.