I have the following standard SDP:

min tr (BX)

s.t. tr(A_iX)\leq b_i, where B,A_i\in C^{n\times n},b_i\in C, X\in S^n and i=1,2,...,m.

For my problem, 1000\leq n\leq10000 and 1000\leq m\leq 10000.

When using CVX with SCS solver, I get out of memory for n=1000. I have about 50 GB RAM.

I would like to know if it is possible to solve problems of this size ?

More importantly, I would like to know the expected memory usage for the above n and m values, as in the expected order (i.e. is it O(n^4+m^2)) ?